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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.
During the last 5 Ma the Earth's ocean-atmosphere system passed through several major transitions, many of which are discussed as possible triggers for human evolution. A classic in this context is the possible influence of the closure of the Panama Strait, the intensification of Northern Hemisphere Glaciation, a stepwise increase in aridity in Africa, and the first appearance of the genus Homo about 2.5 - 2.7 Ma ago. Apart from the fact that the correlation between these events does not necessarily imply causality, many attempts to establish a relationship between climate and evolution fail due to the challenge of precisely localizing an a priori unknown number of changes potentially underlying complex climate records. The kernel-based Bayesian inference approach applied here allows inferring the location, generic shape, and temporal scale of multiple transitions in established records of Plio-Pleistocene African climate. By defining a transparent probabilistic analysis strategy, we are able to identify conjoint changes occurring across the investigated terrigenous dust records from Ocean Drilling Programme (ODP) sites in the Atlantic Ocean (ODP 659), Arabian (ODP 721/722) and Mediterranean Sea (ODP 967). The study indicates a two-step transition in the African climate proxy records at (2.35-2.10) Ma and (1.70 - 1.50) Ma, that may be associated with the reorganization of the Hadley-Walker Circulation. .
Estimating parameters from multiple time series of population dynamics using bayesian inference
(2019)
Empirical time series of interacting entities, e.g., species abundances, are highly useful to study ecological mechanisms. Mathematical models are valuable tools to further elucidate those mechanisms and underlying processes. However, obtaining an agreement between model predictions and experimental observations remains a demanding task. As models always abstract from reality one parameter often summarizes several properties. Parameter measurements are performed in additional experiments independent of the ones delivering the time series. Transferring these parameter values to different settings may result in incorrect parametrizations. On top of that, the properties of organisms and thus the respective parameter values may vary considerably. These issues limit the use of a priori model parametrizations. In this study, we present a method suited for a direct estimation of model parameters and their variability from experimental time series data. We combine numerical simulations of a continuous-time dynamical population model with Bayesian inference, using a hierarchical framework that allows for variability of individual parameters. The method is applied to a comprehensive set of time series from a laboratory predator-prey system that features both steady states and cyclic population dynamics. Our model predictions are able to reproduce both steady states and cyclic dynamics of the data. Additionally to the direct estimates of the parameter values, the Bayesian approach also provides their uncertainties. We found that fitting cyclic population dynamics, which contain more information on the process rates than steady states, yields more precise parameter estimates. We detected significant variability among parameters of different time series and identified the variation in the maximum growth rate of the prey as a source for the transition from steady states to cyclic dynamics. By lending more flexibility to the model, our approach facilitates parametrizations and shows more easily which patterns in time series can be explained also by simple models. Applying Bayesian inference and dynamical population models in conjunction may help to quantify the profound variability in organismal properties in nature.
Recurrence plots and recurrence quantification analysis have become popular in the last two decades. Recurrence based methods have on the one hand a deep foundation in the theory of dynamical systems and are on the other hand powerful tools for the investigation of a variety of problems. The increasing interest encompasses the growing risk of misuse and uncritical application of these methods. Therefore, we point out potential problems and pitfalls related to different aspects of the application of recurrence plots and recurrence quantification analysis.
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.
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 (similar to km) relative displacements with an accuracy of <1 cm/epoch and similar to 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.
During the last decades, increasing exports of both dissolved organic carbon (DOC) and iron were observed from peat catchments in North America and Europe with potential consequences for water quality of streamwater and carbon storages of soils. As mobilisation and transport processes of DOC and iron in peat catchments are only partly understood, the purpose of this study was to elucidate these processes in an intensively monitored and studied system. Specifically, it was hypothesised that dissimilatory iron reduction in riparian peatland soils mobilises DOC initially adsorbed to iron minerals. During stormflow conditions, both DOC and iron will be transported into the stream network. Ferrous iron may be reoxidised at redox interfaces on its way to the stream, and subsequently, ferric iron could be transported together with DOC as complexes. To test these hypotheses, generalised additive models (GAMs) were applied to 14 years of weekly time series of discharge and concentrations of selected solutes measured in a German headwater stream called Lehstenbach. This stream drains a 4.19-km(2) forested mountain catchment; one third of which is covered by riparian peatland soils. We interpreted results of different types of GAM in the way that (a) iron reduction drove the mobilisation of DOC from peatland soils and that (b) both iron and DOC were transported as complexes after their joint mobilisation to and within the steam. It was speculated that low nitrate availability in the uppermost wetland soil layer, particularly during the growing season, promoted iron reduction and thus the mobilisation of DOC. However, the influence of nitrate on the DOC mobilisation remains relatively uncertain. This influence could be further investigated using methods similar to the GAM analysis conducted here for other catchments with long-term data as well as detailed measurements of the relevant species in riparian wetland soils and the adjacent stream network.
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
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