@phdthesis{Forster2021,
  author    = {Forster, Florian},
  title     = {Continuous microgravity monitoring of the Þeistareykir geothermal field (North Iceland)},
  doi       = {10.25932/publishup-54851},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-548517},
  school      = {Universit{\"a}t Potsdam},
  pages     = {XVII, 164},
  year      = {2021},
  abstract  = {In my doctoral thesis, I examine continuous gravity measurements for monitoring of the geothermal site at Þeistareykir in North Iceland. With the help of high-precision superconducting gravity meters (iGravs), I investigate underground mass changes that are caused by operation of the geothermal power plant (i.e. by extraction of hot water and reinjection of cold water). The overall goal of this research project is to make a statement about the sustainable use of the geothermal reservoir, from which also the Icelandic energy supplier and power plant operator Landsvirkjun should benefit. As a first step, for investigating the performance and measurement stability of the gravity meters, in summer 2017, I performed comparative measurements at the gravimetric observatory J9 in Strasbourg. From the three-month gravity time series, I examined calibration, noise and drift behaviour of the iGravs in comparison to stable long-term time series of the observatory superconducting gravity meters. After preparatory work in Iceland (setup of gravity stations, additional measuring equipment and infrastructure, discussions with Landsvirkjun and meetings with the Icelandic partner institute ISOR), gravity monitoring at Þeistareykir was started in December 2017. With the help of the iGrav records of the initial 18 months after start of measurements, I carried out the same investigations (on calibration, noise and drift behaviour) as in J9 to understand how the transport of the superconducting gravity meters to Iceland may influence instrumental parameters. In the further course of this work, I focus on modelling and reduction of local gravity contributions at Þeistareykir. These comprise additional mass changes due to rain, snowfall and vertical surface displacements that superimpose onto the geothermal signal of the gravity measurements. For this purpose, I used data sets from additional monitoring sensors that are installed at each gravity station and adapted scripts for hydro-gravitational modelling. The third part of my thesis targets geothermal signals in the gravity measurements. Together with my PhD colleague Nolwenn Portier from France, I carried out additional gravity measurements with a Scintrex CG5 gravity meter at 26 measuring points within the geothermal field in the summers of 2017, 2018 and 2019. These annual time-lapse gravity measurements are intended to increase the spatial coverage of gravity data from the three continuous monitoring stations to the entire geothermal field. The combination of CG5 and iGrav observations, as well as annual reference measurements with an FG5 absolute gravity meter represent the hybrid gravimetric monitoring method for Þeistareykir. Comparison of the gravimetric data to local borehole measurements (of groundwater levels, geothermal extraction and injection rates) is used to relate the observed gravity changes to the actually extracted (and reinjected) geothermal fluids. An approach to explain the observed gravity signals by means of forward modelling of the geothermal production rate is presented at the end of the third (hybrid gravimetric) study. Further modelling with the help of the processed gravity data is planned by Landsvirkjun. In addition, the experience from time-lapse and continuous gravity monitoring will be used for future gravity measurements at the Krafla geothermal field 22 km south-east of Þeistareykir.},
  language  = {en}
}
@phdthesis{Schmidt2017,
  author    = {Schmidt, Silke Regina},
  title     = {Analyzing lakes in the time frequency domain},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-406955},
  school      = {Universit{\"a}t Potsdam},
  pages     = {VIII, 126},
  year      = {2017},
  abstract  = {The central aim of this thesis is to demonstrate the benefits of innovative frequency-based methods to better explain the variability observed in lake ecosystems. Freshwater ecosystems may be the most threatened part of the hydrosphere. Lake ecosystems are particularly sensitive to changes in climate and land use because they integrate disturbances across their entire catchment. This makes understanding the dynamics of lake ecosystems an intriguing and important research priority. This thesis adds new findings to the baseline knowledge regarding variability in lake ecosystems. It provides a literature-based, data-driven and methodological framework for the investigation of variability and patterns in environmental parameters in the time frequency domain. Observational data often show considerable variability in the environmental parameters of lake ecosystems. This variability is mostly driven by a plethora of periodic and stochastic processes inside and outside the ecosystems. These run in parallel and may operate at vastly different time scales, ranging from seconds to decades. In measured data, all of these signals are superimposed, and dominant processes may obscure the signals of other processes, particularly when analyzing mean values over long time scales. Dominant signals are often caused by phenomena at long time scales like seasonal cycles, and most of these are well understood in the limnological literature. The variability injected by biological, chemical and physical processes operating at smaller time scales is less well understood. However, variability affects the state and health of lake ecosystems at all time scales. Besides measuring time series at sufficiently high temporal resolution, the investigation of the full spectrum of variability requires innovative methods of analysis. Analyzing observational data in the time frequency domain allows to identify variability at different time scales and facilitates their attribution to specific processes. The merit of this approach is subsequently demonstrated in three case studies. The first study uses a conceptual analysis to demonstrate the importance of time scales for the detection of ecosystem responses to climate change. These responses often occur during critical time windows in the year, may exhibit a time lag and can be driven by the exceedance of thresholds in their drivers. This can only be detected if the temporal resolution of the data is high enough. The second study applies Fast Fourier Transform spectral analysis to two decades of daily water temperature measurements to show how temporal and spatial scales of water temperature variability can serve as an indicator for mixing in a shallow, polymictic lake. The final study uses wavelet coherence as a diagnostic tool for limnology on a multivariate high-frequency data set recorded between the onset of ice cover and a cyanobacteria summer bloom in the year 2009 in a polymictic lake. Synchronicities among limnological and meteorological time series in narrow frequency bands were used to identify and disentangle prevailing limnological processes. Beyond the novel empirical findings reported in the three case studies, this thesis aims to more generally be of interest to researchers dealing with now increasingly available time series data at high temporal resolution. A set of innovative methods to attribute patterns to processes, their drivers and constraints is provided to help make more efficient use of this kind of data.},
  language  = {en}
}
@phdthesis{Hendriyana2017,
  author    = {Hendriyana, Andri},
  title     = {Detection and Kirchhoff-type migration of seismic events by use of a new characteristic function},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-398879},
  school      = {Universit{\"a}t Potsdam},
  pages     = {v, 139},
  year      = {2017},
  abstract  = {The classical method of seismic event localization is based on the picking of body wave arrivals, ray tracing and inversion of travel time data. Travel time picks with small uncertainties are required to produce reliable and accurate results with this kind of source localization. Hence recordings, with a low Signal-to-Noise Ratio (SNR) cannot be used in a travel time based inversion. Low SNR can be related with weak signals from distant and/or low magnitude sources as well as with a high level of ambient noise. Diffraction stacking is considered as an alternative seismic event localization method that enables also the processing of low SNR recordings by mean of stacking the amplitudes of seismograms along a travel time function. The location of seismic event and its origin time are determined based on the highest stacked amplitudes (coherency) of the image function. The method promotes an automatic processing since it does not need travel time picks as input data. However, applying diffraction stacking may require longer computation times if only limited computer resources are used. Furthermore, a simple diffraction stacking of recorded amplitudes could possibly fail to locate the seismic sources if the focal mechanism leads to complex radiation patterns which typically holds for both natural and induced seismicity. In my PhD project, I have developed a new work flow for the localization of seismic events which is based on a diffraction stacking approach. A parallelized code was implemented for the calculation of travel time tables and for the determination of an image function to reduce computation time. In order to address the effects from complex source radiation patterns, I also suggest to compute diffraction stacking from a characteristic function (CF) instead of stacking the original wave form data. A new CF, which is called in the following mAIC (modified from Akaike Information Criterion) is proposed. I demonstrate that, the performance of the mAIC does not depend on the chosen length of the analyzed time window and that both P- and S-wave onsets can be detected accurately. To avoid cross-talk between P- and S-waves due to inaccurate velocity models, I separate the P- and S-waves from the mAIC function by making use of polarization attributes. Then, eventually the final image function is represented by the largest eigenvalue as a result of the covariance analysis between P- and S-image functions. Before applying diffraction stacking, I also apply seismogram denoising by using Otsu thresholding in the time-frequency domain. Results from synthetic experiments show that the proposed diffraction stacking provides reliable results even from seismograms with low SNR=1. Tests with different presentations of the synthetic seismograms (displacement, velocity, and acceleration) shown that, acceleration seismograms deliver better results in case of high SNR, whereas displacement seismograms provide more accurate results in case of low SNR recordings. In another test, different measures (maximum amplitude, other statistical parameters) were used to determine the source location in the final image function. I found that the statistical approach is the preferred method particularly for low SNR. The work flow of my diffraction stacking method was finally applied to local earthquake data from Sumatra, Indonesia. Recordings from a temporary network of 42 stations deployed for 9 months around the Tarutung pull-apart Basin were analyzed. The seismic event locations resulting from the diffraction stacking method align along a segment of the Sumatran Fault. A more complex distribution of seismicity is imaged within and around the Tarutung Basin. Two lineaments striking N-S were found in the middle of the Tarutung Basin which support independent results from structural geology. These features are interpreted as opening fractures due to local extension. A cluster of seismic events repeatedly occurred in short time which might be related to fluid drainage since two hot springs are observed at the surface near to this cluster.},
  language  = {en}
}
@phdthesis{Hohenbrink2016,
  author    = {Hohenbrink, Tobias Ludwig},
  title     = {Turning a problem into a solution: heterogeneities in soil hydrology},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-101485},
  school      = {Universit{\"a}t Potsdam},
  pages     = {x, 123},
  year      = {2016},
  abstract  = {It is commonly recognized that soil moisture exhibits spatial heterogeneities occurring in a wide range of scales. These heterogeneities are caused by different factors ranging from soil structure at the plot scale to land use at the landscape scale. There is an urgent need for effi-cient approaches to deal with soil moisture heterogeneity at large scales, where manage-ment decisions are usually made. The aim of this dissertation was to test innovative ap-proaches for making efficient use of standard soil hydrological data in order to assess seep-age rates and main controls on observed hydrological behavior, including the role of soil het-erogeneities. As a first step, the applicability of a simplified Buckingham-Darcy method to estimate deep seepage fluxes from point information of soil moisture dynamics was assessed. This was done in a numerical experiment considering a broad range of soil textures and textural het-erogeneities. The method performed well for most soil texture classes. However, in pure sand where seepage fluxes were dominated by heterogeneous flow fields it turned out to be not applicable, because it simply neglects the effect of water flow heterogeneity. In this study a need for new efficient approaches to handle heterogeneities in one-dimensional water flux models was identified. As a further step, an approach to turn the problem of soil moisture heterogeneity into a solu-tion was presented: Principal component analysis was applied to make use of the variability among soil moisture time series for analyzing apparently complex soil hydrological systems. It can be used for identifying the main controls on the hydrological behavior, quantifying their relevance, and describing their particular effects by functional averaged time series. The ap-proach was firstly tested with soil moisture time series simulated for different texture classes in homogeneous and heterogeneous model domains. Afterwards, it was applied to 57 mois-ture time series measured in a multifactorial long term field experiment in Northeast Germa-ny. The dimensionality of both data sets was rather low, because more than 85 \% of the total moisture variance could already be explained by the hydrological input signal and by signal transformation with soil depth. The perspective of signal transformation, i.e. analyzing how hydrological input signals (e.g., rainfall, snow melt) propagate through the vadose zone, turned out to be a valuable supplement to the common mass flux considerations. Neither different textures nor spatial heterogeneities affected the general kind of signal transfor-mation showing that complex spatial structures do not necessarily evoke a complex hydro-logical behavior. In case of the field measured data another 3.6\% of the total variance was unambiguously explained by different cropping systems. Additionally, it was shown that dif-ferent soil tillage practices did not affect the soil moisture dynamics at all. The presented approach does not require a priori assumptions about the nature of physical processes, and it is not restricted to specific scales. Thus, it opens various possibilities to in-corporate the key information from monitoring data sets into the modeling exercise and thereby reduce model uncertainties.},
  language  = {en}
}
@phdthesis{Kuetter2015,
  author    = {K{\"u}tter, Sissy},
  title     = {Magnetotelluric measurements across the southern Barberton Greenstone Belt, South Africa},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-83198},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xix, 156},
  year      = {2015},
  abstract  = {Der Barberton Gr{\"u}nsteing{\"u}rtel (BGB) in S{\"u}dafrika geh{\"o}rt zu den wenigen Regionen mit noch gut erhaltener Archaischer Kruste. Seit Jahrhunderten wurde der BGB eingehend untersucht und seine geologischen und tektonischen Strukturen detailliert kartiert. {\"U}ber die tiefere Struktur des BGB ist hingegen wenig bekannt. Zahlreiche Evolutionsmodelle, die auf Altersbestimmungsdaten und strukturellen Informationen beruhen wurden {\"u}ber die Jahre aufgestellt. Diese Theorien sind zumeist widerspr{\"u}chlich. Sie konzentrieren sich im Wesentlichen auf die Frage, ob plattentektonische Prozesse bereits bei der Entwicklung der fr{\"u}hen Erde eine Rolle spielten oder ob vertikale Tektonik, angetrieben durch die im Archaikum h{\"o}heren Temperaturen, die Bildung der heutigen Kontinente bestimmt hat. Um neue Erkenntnisse {\"u}ber die interne Struktur und Entwicklungsgeschichte des BGB zu erhalten, wurden im Rahmen der Deutsch-S{\"u}dafrikanischen Forschungsinitiative Inkaba yeAfrica magnetotellurische (MT) Messungen durchgef{\"u}hrt. Entlang von sechs Profilen, die den gesamten s{\"u}dlichen Teil des BGB's {\"u}berdecken, wurden nahezu 200 MT-Stationen installiert. Tektonische Strukturen wie z. B. (fossile) Verwerfungszonen k{\"o}nnen erh{\"o}hte Leitf{\"a}higigkeiten haben, wenn sich leitf{\"a}hige Mineralisationen innerhalb der Scherzonen gebildet haben. Durch die Abbildung der elektrischen Leitf{\"a}higkeitsverteilung des Untergrundes mit Hilfe von MT Messungen kann der Verlauf tektonischer Strukturen nachvollzogen werden, woraus Schl{\"u}sse {\"u}ber m{\"o}glicherweise abgelaufene tektonische Prozesse gezogen werden k{\"o}nnen. Der gesamte MT Datensatz weist starke St{\"o}reinfl{\"u}sse durch k{\"u}nstliche elektromagnetische Signale auf, die bspw. von Stromleitungen und elektrischen Z{\"a}unen stammen. Insbesondere langperiodische Daten (>1 s) sind davon betroffen, die f{\"u}r die Aufl{\"o}sung tieferer Strukturen notwendig sind. Die Anwendung etablierter Ans{\"a}tze wie Verschiebungsfiltern und der Remote Reference-Methode, f{\"u}hrte zu Verbesserungen vorrangig f{\"u}r Perioden < 1 s. Der langperiodische Bereich ist durch impulsartige St{\"o}rsignale in den magnetischen und dazugeh{\"o}rigen Stufen in den elektrischen Feldkomponenten gepr{\"a}gt. Im Rahmen dieser Arbeit wurde ein neuartiger Zeitbereichs-Filter entwickelt, welcher auf einer abgewandelten Form des Wiener Filters beruht und diese Art von St{\"o}rsignalen aus den Daten entfernt. Durch den Vergleich der Datenvarianz einer lokalen Station mit der einer Referenzstation k{\"o}nnen gest{\"o}rte Zeitsegmente identifiziert werden. Anschließend wird ein Wiener-Filter-Algorithmus angewendet, um f{\"u}r diese Segmente mithilfe der Referenzdaten physikalisch sinnvolle Zeitreihen zu berechnen, mit denen die Daten der lokalen Station ersetzt werden. W{\"a}hrend impulsartige St{\"o}rsignale in den magnetischen Datenkan{\"a}len relativ einfach erfasst werden k{\"o}nnen, ist die Detektion von Vers{\"a}tzen in den elektrischen Zeitreihen je nach Versatzh{\"o}he problematischer. Um dieses Problem zu umgehen, habe ich einen Algorithmus entwickelt, bei dem die Zeitreihen differenziert, gefiltert und im letzten Schritt integriert werden. In einer zweiten von mir entwickelten Filtermethode werden die St{\"o}rsignale durch den Vergleich des kurzzeitigen und des langzeitigen Datenmittelwerts ausfindig gemacht. Bei diesem Filter werden die St{\"o}rsignale aus den Zeitreihen entfernt und durch eine lineare Interpolation ersetzt. Durch die beiden Filtermethoden wurde eine deutliche Verbesserung der Datenqualit{\"a}t bis zu 10 und teilweise 100 s erreicht. Zur Interpretation des MT-Datensatzes wurden 2D und 3D Inversionen durchgef{\"u}hrt. Die so erhaltenen elektrischen Leitf{\"a}higkeitsmodelle zeigen eine gute {\"U}bereinstimmung mit den kartierten, geologischen Strukturen. Die Gesteine des BGB weisen in den Modellen hohe Widerst{\"a}nde auf und sind deutlich von leitf{\"a}higen benachbarten geologischen Strukturen abgegrenzt. Verwerfungszonen korrelieren mit leitf{\"a}higen Strukturen, die sich bis in eine Tiefe von 5 bis 10 km erstrecken. Eine Fortsetzung der Verwerfungszonen {\"u}ber die s{\"u}dliche Grenze des BGB wird in den 2D-Ergebnissen angedeutet. Insgesamt zeigen die Inversionsmodelle, dass vermutlich sowohl plattentektonische als auch vertikaltektonische Prozesse bei der Entstehung des BGB eine wichtige Rolle spielten.},
  language  = {en}
}
@phdthesis{Schwabedal2010,
  author    = {Schwabedal, Justus Tilmann Caspar},
  title     = {Phase dynamics of irregular oscillations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-50115},
  school      = {Universit{\"a}t Potsdam},
  year      = {2010},
  abstract  = {In der vorliegenden Dissertation wird eine Beschreibung der Phasendynamik irregul{\"a}rer Oszillationen und deren Wechselwirkungen vorgestellt. Hierbei werden chaotische und stochastische Oszillationen autonomer dissipativer Systeme betrachtet. F{\"u}r eine Phasenbeschreibung stochastischer Oszillationen m{\"u}ssen zum einen unterschiedliche Werte der Phase zueinander in Beziehung gesetzt werden, um ihre Dynamik unabh{\"a}ngig von der gew{\"a}hlten Parametrisierung der Oszillation beschreiben zu k{\"o}nnen. Zum anderen m{\"u}ssen f{\"u}r stochastische und chaotische Oszillationen diejenigen Systemzust{\"a}nde identifiziert werden, die sich in der gleichen Phase befinden. Im Rahmen dieser Dissertation werden die Werte der Phase {\"u}ber eine gemittelte Phasengeschwindigkeitsfunktion miteinander in Beziehung gesetzt. F{\"u}r stochastische Oszillationen sind jedoch verschiedene Definitionen der mittleren Geschwindigkeit m{\"o}glich. Um die Unterschiede der Geschwindigkeitsdefinitionen besser zu verstehen, werden auf ihrer Basis effektive deterministische Modelle der Oszillationen konstruiert. Hierbei zeigt sich, dass die Modelle unterschiedliche Oszillationseigenschaften, wie z. B. die mittlere Frequenz oder die invariante Wahrscheinlichkeitsverteilung, nachahmen. Je nach Anwendung stellt die effektive Phasengeschwindigkeitsfunktion eines speziellen Modells eine zweckm{\"a}ßige Phasenbeziehung her. Wie anhand einfacher Beispiele erkl{\"a}rt wird, kann so die Theorie der effektiven Phasendynamik auch kontinuierlich und pulsartig wechselwirkende stochastische Oszillationen beschreiben. Weiterhin wird ein Kriterium f{\"u}r die invariante Identifikation von Zust{\"a}nden gleicher Phase irregul{\"a}rer Oszillationen zu sogenannten generalisierten Isophasen beschrieben: Die Zust{\"a}nde einer solchen Isophase sollen in ihrer dynamischen Entwicklung ununterscheidbar werden. F{\"u}r stochastische Oszillationen wird dieses Kriterium in einem mittleren Sinne interpretiert. Wie anhand von Beispielen demonstriert wird, lassen sich so verschiedene Typen stochastischer Oszillationen in einheitlicher Weise auf eine stochastische Phasendynamik reduzieren. Mit Hilfe eines numerischen Algorithmus zur Sch{\"a}tzung der Isophasen aus Daten wird die Anwendbarkeit der Theorie anhand eines Signals regelm{\"a}ßiger Atmung gezeigt. Weiterhin zeigt sich, dass das Kriterium der Phasenidentifikation f{\"u}r chaotische Oszillationen nur approximativ erf{\"u}llt werden kann. Anhand des R{\"o}ssleroszillators wird der tiefgreifende Zusammenhang zwischen approximativen Isophasen, chaotischer Phasendiffusion und instabilen periodischen Orbits dargelegt. Gemeinsam erm{\"o}glichen die Theorien der effektiven Phasendynamik und der generalisierten Isophasen eine umfassende und einheitliche Phasenbeschreibung irregul{\"a}rer Oszillationen.},
  language  = {de}
}
@phdthesis{Donner2006,
  author    = {Donner, Reik Volker},
  title     = {Advanced methods for analysing and modelling multivariate palaeoclimatic time series},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-12560},
  school      = {Universit{\"a}t Potsdam},
  year      = {2006},
  abstract  = {The separation of natural and anthropogenically caused climatic changes is an important task of contemporary climate research. For this purpose, a detailed knowledge of the natural variability of the climate during warm stages is a necessary prerequisite. Beside model simulations and historical documents, this knowledge is mostly derived from analyses of so-called climatic proxy data like tree rings or sediment as well as ice cores. In order to be able to appropriately interpret such sources of palaeoclimatic information, suitable approaches of statistical modelling as well as methods of time series analysis are necessary, which are applicable to short, noisy, and non-stationary uni- and multivariate data sets. Correlations between different climatic proxy data within one or more climatological archives contain significant information about the climatic change on longer time scales. Based on an appropriate statistical decomposition of such multivariate time series, one may estimate dimensions in terms of the number of significant, linear independent components of the considered data set. In the presented work, a corresponding approach is introduced, critically discussed, and extended with respect to the analysis of palaeoclimatic time series. Temporal variations of the resulting measures allow to derive information about climatic changes. For an example of trace element abundances and grain-size distributions obtained near the Cape Roberts (Eastern Antarctica), it is shown that the variability of the dimensions of the investigated data sets clearly correlates with the Oligocene/Miocene transition about 24 million years before present as well as regional deglaciation events. Grain-size distributions in sediments give information about the predominance of different transportation as well as deposition mechanisms. Finite mixture models may be used to approximate the corresponding distribution functions appropriately. In order to give a complete description of the statistical uncertainty of the parameter estimates in such models, the concept of asymptotic uncertainty distributions is introduced. The relationship with the mutual component overlap as well as with the information missing due to grouping and truncation of the measured data is discussed for a particular geological example. An analysis of a sequence of grain-size distributions obtained in Lake Baikal reveals that there are certain problems accompanying the application of finite mixture models, which cause an extended climatological interpretation of the results to fail. As an appropriate alternative, a linear principal component analysis is used to decompose the data set into suitable fractions whose temporal variability correlates well with the variations of the average solar insolation on millenial to multi-millenial time scales. The abundance of coarse-grained material is obviously related to the annual snow cover, whereas a significant fraction of fine-grained sediments is likely transported from the Taklamakan desert via dust storms in the spring season.},
  language  = {en}
}
@phdthesis{Maraun2006,
  author    = {Maraun, Douglas},
  title     = {What can we learn from climate data? : Methods for fluctuation, time/scale and phase analysis},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-9047},
  school      = {Universit{\"a}t Potsdam},
  year      = {2006},
  abstract  = {Since Galileo Galilei invented the first thermometer, researchers have tried to understand the complex dynamics of ocean and atmosphere by means of scientific methods. They observe nature and formulate theories about the climate system. Since some decades powerful computers are capable to simulate the past and future evolution of climate. Time series analysis tries to link the observed data to the computer models: Using statistical methods, one estimates characteristic properties of the underlying climatological processes that in turn can enter the models. The quality of an estimation is evaluated by means of error bars and significance testing. On the one hand, such a test should be capable to detect interesting features, i.e. be sensitive. On the other hand, it should be robust and sort out false positive results, i.e. be specific. This thesis mainly aims to contribute to methodological questions of time series analysis with a focus on sensitivity and specificity and to apply the investigated methods to recent climatological problems. First, the inference of long-range correlations by means of Detrended Fluctuation Analysis (DFA) is studied. It is argued that power-law scaling of the fluctuation function and thus long-memory may not be assumed a priori but have to be established. This requires to investigate the local slopes of the fluctuation function. The variability characteristic for stochastic processes is accounted for by calculating empirical confidence regions. The comparison of a long-memory with a short-memory model shows that the inference of long-range correlations from a finite amount of data by means of DFA is not specific. When aiming to infer short memory by means of DFA, a local slope larger than \$\alpha=0.5\$ for large scales does not necessarily imply long-memory. Also, a finite scaling of the autocorrelation function is shifted to larger scales in the fluctuation function. It turns out that long-range correlations cannot be concluded unambiguously from the DFA results for the Prague temperature data set. In the second part of the thesis, an equivalence class of nonstationary Gaussian stochastic processes is defined in the wavelet domain. These processes are characterized by means of wavelet multipliers and exhibit well defined time dependent spectral properties; they allow one to generate realizations of any nonstationary Gaussian process. The dependency of the realizations on the wavelets used for the generation is studied, bias and variance of the wavelet sample spectrum are calculated. To overcome the difficulties of multiple testing, an areawise significance test is developed and compared to the conventional pointwise test in terms of sensitivity and specificity. Applications to Climatological and Hydrological questions are presented. The thesis at hand mainly aims to contribute to methodological questions of time series analysis and to apply the investigated methods to recent climatological problems. In the last part, the coupling between El Nino/Southern Oscillation (ENSO) and the Indian Monsoon on inter-annual time scales is studied by means of Hilbert transformation and a curvature defined phase. This method allows one to investigate the relation of two oscillating systems with respect to their phases, independently of their amplitudes. The performance of the technique is evaluated using a toy model. From the data, distinct epochs are identified, especially two intervals of phase coherence, 1886-1908 and 1964-1980, confirming earlier findings from a new point of view. A significance test of high specificity corroborates these results. Also so far unknown periods of coupling invisible to linear methods are detected. These findings suggest that the decreasing correlation during the last decades might be partly inherent to the ENSO/Monsoon system. Finally, a possible interpretation of how volcanic radiative forcing could cause the coupling is outlined.},
  subject      = {Spektralanalyse <Stochastik>},
  language  = {en}
}
@book{Strohe2004,
  author    = {Strohe, Hans Gerhard},
  title     = {Time series analysis},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-6601},
  publisher      = {Universit{\"a}t Potsdam},
  year      = {2004},
  subject      = {Zeitreihenanalyse},
  language  = {en}
}
@phdthesis{RomanoBlasco2004,
  author    = {Romano Blasco, M. Carmen},
  title     = {Synchronization analysis by means of recurrences in phase space},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-0001756},
  school      = {Universit{\"a}t Potsdam},
  year      = {2004},
  abstract  = {Die t{\"a}gliche Erfahrung zeigt uns, daß bei vielen physikalischen Systemen kleine {\"A}nderungen in den Anfangsbedingungen auch zu kleinen {\"A}nderungen im Verhalten des Systems f{\"u}hren. Wenn man z.B. das Steuerrad beim Auto fahren nur ein wenig zur Seite dreht, unterscheidet sich die Richtung des Wagens auch nur wenig von der urspr{\"u}nglichen Richtung. Aber es gibt auch Situationen, f{\"u}r die das Gegenteil dieser Regel zutrifft. Die Folge von Kopf und Zahl, die wir erhalten, wenn wir eine M{\"u}nze werfen, zeigt ein irregul{\"a}res oder chaotisches Zeitverhalten, da winzig kleine {\"A}nderungen in den Anfangsbedingungen, die z.B. durch leichte Drehung der Hand hervorgebracht werden, zu vollkommen verschiedenen Resultaten f{\"u}hren. In den letzten Jahren hat man sehr viele nichtlineare Systeme mit schnellen Rechnern untersucht und festgestellt, daß eine sensitive Abh{\"a}ngigkeit von den Anfangsbedingungen, die zu einem chaotischen Verhalten f{\"u}hrt, keinesfalls die Ausnahme darstellt, sondern eine typische Eigenschaft vieler Systeme ist. Obwohl chaotische Systeme kleinen {\"A}nderungen in den Anfangsbedingungen gegen{\"u}ber sehr empfindlich reagieren, k{\"o}nnen sie synchronisieren wenn sie durch eine gemeinsame {\"a}ußere Kraft getrieben werden, oder wenn sie miteinander gekoppelt sind. Das heißt, sie vergessen ihre Anfangsbedingungen und passen ihre Rhythmen aneinander. Diese Eigenschaft chaotischer Systeme hat viele Anwendungen, wie z.B. das Design von Kommunikationsger{\"a}te und die verschl{\"u}sselte {\"U}bertragung von Mitteilungen. Abgesehen davon, findet man Synchronisation in nat{\"u}rlichen Systemen, wie z.B. das Herz-Atmungssystem, raumverteilte {\"o}kologische Systeme, die Magnetoenzephalographische Aktivit{\"a}t von Parkinson Patienten, etc. In solchen komplexen Systemen ist es nicht trivial Synchronisation zu detektieren und zu quantifizieren. Daher ist es notwendig, besondere mathematische Methoden zu entwickeln, die diese Aufgabe erledigen. Das ist das Ziel dieser Arbeit. Basierend auf dergrundlegenden Idee von Rekurrenzen (Wiederkehr) von Trajektorien dynamischer Systeme, sind verschiedene Maße entwickelt worden, die Synchronisation in chaotischen und komplexen Systemen detektieren. Das Wiederkehr von Trajektorien erlaubt uns Vorhersagen {\"u}ber den zuk{\"u}nftigen Zustand eines Systems zu treffen. Wenn man diese Eigenschaft der Wiederkehr von zwei interagierenden Systemen vergleicht, kann man Schl{\"u}sse {\"u}ber ihre dynamische Anpassung oder Synchronisation ziehen. Ein wichtiger Vorteil der Rekurrenzmaße f{\"u}r Synchronisation ist die Robustheit gegen Rauschen und Instationari{\"a}t. Das erlaubt eine Synchronisationsanalyse in Systemen durchzuf{\"u}hren, die bisher nicht darauf untersucht werden konnten.},
  language  = {en}
}