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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.
The intrinsic predictability of ecological time series and its potential to guide forecasting
(2019)
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.
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.
Hydrological models are commonly used to perform real-time runoff forecasting for flood warning. Their application requires catchment characteristics and precipitation series that are not always available. An alternative approach is nonparametric modelling based only on runoff series. However, the following questions arise: Can nonparametric models show reliable forecasting? Can they perform as reliably as hydrological models? We performed probabilistic forecasting one, two and three hours ahead for a runoff series, with the aim of ascribing a probability density function to predicted discharge using time series analysis based on stochastic dynamics theory. The derived dynamic terms were compared to a hydrological model, LARSIM. Our procedure was able to forecast within 95% confidence interval 1-, 2- and 3-h ahead discharge probability functions with about 1.40 m(3)/s of range and relative errors (%) in the range [-30; 30]. The LARSIM model and the best nonparametric approaches gave similar results, but the range of relative errors was larger for the nonparametric approaches.
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.
With the advent of the two Sentinel-1 (S1) satellites, Synthetic Aperture Radar (SAR) data with high temporal and spatial resolution are freely available. This provides a promising framework to facilitate detailed investigations of surface instabilities and movements on large scales with high temporal resolution, but also poses substantial processing challenges because of storage and computation requirements. Methods are needed to efficiently detect short term changes in dynamic environments. Approaches considering pair-wise processing of a series of consecutive scenes to retain maximum temporal resolution in conjunction with time series analyses are required. Here we present OSARIS, the “Open Source SAR Investigation System,” as a framework to process large stacks of S1 data on high-performance computing clusters. Based on Generic Mapping Tools SAR, shell scripts, and the workload manager Slurm, OSARIS provides an open and modular framework combining parallelization of high-performance C programs, flexible processing schemes, convenient configuration, and generation of geocoded stacks of analysis-ready base data, including amplitude, phase, coherence, and unwrapped interferograms. Time series analyses can be conducted by applying automated modules to the data stacks. The capabilities of OSARIS are demonstrated in a case study from the northwestern Tien Shan, Central Asia. After merging of slices, a total of 80 scene pairs were processed from 174 total input scenes. The coherence time series exhibits pronounced seasonal variability, with relatively high coherence values prevailing during the summer months in the nival zone. As an example of a time series analysis module, we present OSARIS' “Unstable Coherence Metric” which identifies pixels affected by significant drops from high to low coherence values. Measurements of motion provided by LOSD measurements require careful evaluation because interferometric phase unwrapping is prone to errors. Here, OSARIS provides a series of modules to detect and mask unwrapping errors, correct for atmospheric disturbances, and remove large-scale trends. Wall clock processing time for the case study (area ~9,000 km2) was ~12 h 4 min on a machine with 400 cores and 2 TB RAM. In total, ~12 d 10 h 44 min (~96%) were saved through parallelization. A comparison of selected OSARIS datasets to results from two state-of-the-art SAR processing suites, ISCE and SNAP, shows that OSARIS provides products of competitive quality despite its high level of automatization. OSARIS thus facilitates efficient S1-based region-wide investigations of surface movement events over multiple years.
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
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.