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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.
LiCSBAS
(2020)
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.
The Barberton Greenstone Belt (BGB) in the northwestern part of South Africa belongs to the few well-preserved remnants of Archean crust. Over the last centuries, the BGB has been intensively studied at surface with detailed mapping of its surfacial geological units and tectonic features. Nevertheless, the deeper structure of the BGB remains poorly understood. Various tectonic evolution models have been developed based on geo-chronological and structural data. These theories are highly controversial and centre on the question whether plate tectonics - as geoscientists understand them today - was already evolving on the Early Earth or whether vertical mass movements driven by the higher temperature of the Earth in Archean times governed continent development.
To get a step closer to answering the questions regarding the internal structure and formation of the BGB, magnetotelluric (MT) field experiments were conducted as part of the German-South African research initiative Inkaba yeAfrica. Five-component MT data (three magnetic and two electric channels) were collected at ~200 sites aligned along six profiles crossing the southern part of the BGB. Tectonic features like (fossil) faults and shear zones are often mineralized and therefore can have high electrical conductivities. Hence, by obtaining an image of the conductivity distribution of the subsurface from MT measurements can provide useful information on tectonic processes.
Unfortunately, the BGB MT data set is heavily affected by man-made electromagnetic noise caused, e.g. by powerlines and electric fences. Aperiodic spikes in the magnetic and corresponding offsets in the electric field components impair the data quality particularly at periods >1 s which are required to image deep electrical structures. Application of common methods for noise reduction like delay filtering and remote reference processing, only worked well for periods <1 s. Within the framework of this thesis two new filtering approaches were developed to handle the severe noise in long period data and obtain reliable processing results. The first algorithm is based on the Wiener filter in combination with a spike detection algorithm. Comparison of data variances of a local site with those of a reference site allows the identification of disturbed time series windows for each recorded channel at the local site. Using the data of the reference site, a Wiener filter algorithm is applied to predict physically meaningful data to replace the disturbed windows. While spikes in the magnetic channels are easily recognized and replaced, steps in the electric channels are more difficult to detect depending on their offset. Therefore, I have implemented a novel approach based on time series differentiation, noise removal and subsequent integration to overcome this obstacle. A second filtering approach where spikes and steps in the time series are identified using a comparison of the short and long time average of the data was also implemented as part of my thesis. For this filtering approach the noise in the form of spikes and offsets in the data is treated by an interpolation of the affected data samples. The new developments resulted in a substantial data improvement and allowed to gain one to two decades of data (up to 10 or 100 s).
The re-processed MT data were used to image the electrical conductivity distribution of the BGB by 2D and 3D inversion. Inversion models are in good agreement with the surface geology delineating the highly resistive rocks of the BGB from surrounding more conductive geological units. Fault zones appear as conductive structures and can be traced to depths of 5 to 10 km. 2D models suggest a continuation of the faults further south across the boundary of the BGB. Based on the shallow tectonic structures (fault system) within the BGB compared to deeply rooted resistive batholiths in the area, tectonic models including both vertical mass transport and in parts present-day style plate tectonics seem to be most likely for the evolution of the BGB.
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
In der vorliegenden Dissertation wird eine Beschreibung der Phasendynamik irregulärer Oszillationen und deren Wechselwirkungen vorgestellt. Hierbei werden chaotische und stochastische Oszillationen autonomer dissipativer Systeme betrachtet. Für eine Phasenbeschreibung stochastischer Oszillationen müssen zum einen unterschiedliche Werte der Phase zueinander in Beziehung gesetzt werden, um ihre Dynamik unabhängig von der gewählten Parametrisierung der Oszillation beschreiben zu können. Zum anderen müssen für stochastische und chaotische Oszillationen diejenigen Systemzustände identifiziert werden, die sich in der gleichen Phase befinden. Im Rahmen dieser Dissertation werden die Werte der Phase über eine gemittelte Phasengeschwindigkeitsfunktion miteinander in Beziehung gesetzt. Für stochastische Oszillationen sind jedoch verschiedene Definitionen der mittleren Geschwindigkeit möglich. 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 zweckmäßige Phasenbeziehung her. Wie anhand einfacher Beispiele erklärt wird, kann so die Theorie der effektiven Phasendynamik auch kontinuierlich und pulsartig wechselwirkende stochastische Oszillationen beschreiben. Weiterhin wird ein Kriterium für die invariante Identifikation von Zuständen gleicher Phase irregulärer Oszillationen zu sogenannten generalisierten Isophasen beschrieben: Die Zustände einer solchen Isophase sollen in ihrer dynamischen Entwicklung ununterscheidbar werden. Für 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 Schätzung der Isophasen aus Daten wird die Anwendbarkeit der Theorie anhand eines Signals regelmäßiger Atmung gezeigt. Weiterhin zeigt sich, dass das Kriterium der Phasenidentifikation für chaotische Oszillationen nur approximativ erfüllt werden kann. Anhand des Rössleroszillators wird der tiefgreifende Zusammenhang zwischen approximativen Isophasen, chaotischer Phasendiffusion und instabilen periodischen Orbits dargelegt. Gemeinsam ermöglichen die Theorien der effektiven Phasendynamik und der generalisierten Isophasen eine umfassende und einheitliche Phasenbeschreibung irregulärer Oszillationen.
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.
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.