@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}
}
@misc{MorishitaLazeckyWrightetal.2020,
  author    = {Morishita, Yu and Lazecky, Milan and Wright, Tim J. and Weiss, Jonathan R. and Elliott, John R. and Hooper, Andy},
  title     = {LiCSBAS},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {1078},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-47243},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472431},
  pages     = {31},
  year      = {2020},
  abstract  = {For the past five years, the 2-satellite Sentinel-1 constellation has provided abundant and useful Synthetic Aperture Radar (SAR) data, which have the potential to reveal global ground surface deformation at high spatial and temporal resolutions. However, for most users, fully exploiting the large amount of associated data is challenging, especially over wide areas. To help address this challenge, we have developed LiCSBAS, an open-source SAR interferometry (InSAR) time series analysis package that integrates with the automated Sentinel-1 InSAR processor (LiCSAR). LiCSBAS utilizes freely available LiCSAR products, and users can save processing time and disk space while obtaining the results of InSAR time series analysis. In the LiCSBAS processing scheme, interferograms with many unwrapping errors are automatically identified by loop closure and removed. Reliable time series and velocities are derived with the aid of masking using several noise indices. The easy implementation of atmospheric corrections to reduce noise is achieved with the Generic Atmospheric Correction Online Service for InSAR (GACOS). Using case studies in southern Tohoku and the Echigo Plain, Japan, we demonstrate that LiCSBAS applied to LiCSAR products can detect both large-scale (>100 km) and localized (~km) relative displacements with an accuracy of <1 cm/epoch and ~2 mm/yr. We detect displacements with different temporal characteristics, including linear, periodic, and episodic, in Niigata, Ojiya, and Sanjo City, respectively. LiCSBAS and LiCSAR products facilitate greater exploitation of globally available and abundant SAR datasets and enhance their applications for scientific research and societal benefit.},
  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}
}
@misc{RungeGrosse2020,
  author    = {Runge, Alexandra and Grosse, Guido},
  title     = {Mosaicking Landsat and Sentinel-2 Data to Enhance LandTrendr Time Series Analysis in Northern High Latitude Permafrost Regions},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {1009},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-48031},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-480317},
  pages     = {25},
  year      = {2020},
  abstract  = {Permafrost is warming in the northern high latitudes, inducing highly dynamic thaw-related permafrost disturbances across the terrestrial Arctic. Monitoring and tracking of permafrost disturbances is important as they impact surrounding landscapes, ecosystems and infrastructure. Remote sensing provides the means to detect, map, and quantify these changes homogeneously across large regions and time scales. Existing Landsat-based algorithms assess different types of disturbances with similar spatiotemporal requirements. However, Landsat-based analyses are restricted in northern high latitudes due to the long repeat interval and frequent clouds, in particular at Arctic coastal sites. We therefore propose to combine Landsat and Sentinel-2 data for enhanced data coverage and present a combined annual mosaic workflow, expanding currently available algorithms, such as LandTrendr, to achieve more reliable time series analysis. We exemplary test the workflow for twelve sites across the northern high latitudes in Siberia. We assessed the number of images and cloud-free pixels, the spatial mosaic coverage and the mosaic quality with spectral comparisons. The number of available images increased steadily from 1999 to 2019 but especially from 2016 onward with the addition of Sentinel-2 images. Consequently, we have an increased number of cloud-free pixels even under challenging environmental conditions, which then serve as the input to the mosaicking process. In a comparison of annual mosaics, the Landsat+Sentinel-2 mosaics always fully covered the study areas (99.9-100 \%), while Landsat-only mosaics contained data-gaps in the same years, only reaching coverage percentages of 27.2 \%, 58.1 \%, and 69.7 \% for Sobo Sise, East Taymyr, and Kurungnakh in 2017, respectively. The spectral comparison of Landsat image, Sentinel-2 image, and Landsat+Sentinel-2 mosaic showed high correlation between the input images and mosaic bands (e.g., for Kurungnakh 0.91-0.97 between Landsat and Landsat+Sentinel-2 mosaic and 0.92-0.98 between Sentinel-2 and Landsat+Sentinel-2 mosaic) across all twelve study sites, testifying good quality mosaic results. Our results show that especially the results for northern, coastal areas was substantially improved with the Landsat+Sentinel-2 mosaics. By combining Landsat and Sentinel-2 data we accomplished to create reliably high spatial resolution input mosaics for time series analyses. Our approach allows to apply a high temporal continuous time series analysis to northern high latitude permafrost regions for the first time, overcoming substantial data gaps, and assess permafrost disturbance dynamics on an annual scale across large regions with algorithms such as LandTrendr by deriving the location, timing and progression of permafrost thaw disturbances},
  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}
}
@misc{ŚlęzakBurneckiMetzler2019,
  author    = {Ślęzak, Jakub and Burnecki, Krzysztof and Metzler, Ralf},
  title     = {Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems},
  series = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe},
  number    = {765},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-43792},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-437923},
  pages     = {18},
  year      = {2019},
  abstract  = {Many studies on biological and soft matter systems report the joint presence of a linear mean-squared displacement and a non-Gaussian probability density exhibiting, for instance, exponential or stretched-Gaussian tails. This phenomenon is ascribed to the heterogeneity of the medium and is captured by random parameter models such as 'superstatistics' or 'diffusing diffusivity'. Independently, scientists working in the area of time series analysis and statistics have studied a class of discrete-time processes with similar properties, namely, random coefficient autoregressive models. In this work we try to reconcile these two approaches and thus provide a bridge between physical stochastic processes and autoregressive models.Westart from the basic Langevin equation of motion with time-varying damping or diffusion coefficients and establish the link to random coefficient autoregressive processes. By exploring that link we gain access to efficient statistical methods which can help to identify data exhibiting Brownian yet non-Gaussian diffusion.},
  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}
}