ABSTRACT Since the advent of the satellite era, global sea-level altimetry data sets are availabl... more ABSTRACT Since the advent of the satellite era, global sea-level altimetry data sets are available. To study complex oceanographic processes and their coupling to atmospheric dynamics it is necessary to advance beyond analyzing global mean sea-level rise or local trends. We apply a wide range of methods from linear and nonlinear time series analysis for investigating the complex dynamics of observed sea-level altimetry time series at different locations around the globe. Employing this toolkit, linear and nonlinear autodependencies (autocorrelation and auto-mutual information functions), deterministic structure (recurrence quantification and recurrence network analysis), time-reversibility characteristics (visibility graph analysis) and the relative importance of stochastic vs. deterministic dynamics (complexity-entropy plane) are studied. Combining the complimentary information from all metrics, consistent spatial patterns of sea-level dynamics are detected. Classical statistical properties such as variance, skewness and Shannon entropy of the probability distribution of sea-level reveal the special importance of western boundary currents as well as parts of the Antarctic Circumpolar Current as regions of particularly complex sea-level dynamics. In turn, the nonlinear dynamics characteristics present a somewhat different pattern exhibiting particularly high complexity in the tropics as well as the Gulf Stream and Kuroshio regions. Notably, these are also the areas where missing values due to atmospheric processes are most prominent. Further research is required to fully disentangle the dynamic complexity of sea-level from potential artifacts in the underlying altimetry data.
ABSTRACT Recent work on sea-level change has mainly focused on long-term trends in the mean. In t... more ABSTRACT Recent work on sea-level change has mainly focused on long-term trends in the mean. In turn, changes in the nonlinear dynamics of sea-level variability have hardly been studied so far, even though they can provide unique information on the ocean's response to long-term changes of different atmospheric driving factors. In this work, we study seven long-term daily tide gauge records from the Baltic Sea with a set of complementary methods of linear and nonlinear time series analysis, including discrete wavelet analysis, autocorrelation-based dimension densities, time- and scale-dependent detrended fluctuation analysis, measures of complexity based on recurrence quantification analysis and recurrence networks, as well as information-theoretic approaches. The linear and nonlinear dynamical properties obtained for different records show consistent long-term variations, which are determined by changes in both local hydrological factors and the regional climatology. Time- and scale-resolved analyses reveal that temporal changes of nonlinear dynamic characteristics affect different temporal scales in different ways and are thus reflected differently by the individual measures evaluated at distinct scales. The corresponding analysis allows identifying and distinguishing long-term changes in sub-annual as well as annual to decadal-scale variability, which can be related to triggering factors acting at different temporal scales. In general, the results of all applied analyses display a consistent spatial pattern with a marked latitudinal complexity gradient, with sea-level variability being most complex close to the Baltic entrance and least complex in the central Baltic Sea.
Stream flow observations from a geographical region are known to often exhibit strong common beha... more Stream flow observations from a geographical region are known to often exhibit strong common behavior. In order to assess the temporal evolution of the complexity of stream flow time series from all over Europe, we employ the recently developed Linear Variance Decay dimension density (^LV D). It is estimated as the parameter of an exponential decay function fitted to the
Singular System Analysis (SSA) is a powerful data-oriented time series decomposition tool used e.... more Singular System Analysis (SSA) is a powerful data-oriented time series decomposition tool used e.g. in atmospheric physics and hydrology to extract the dynamics contained in time series at arbitrary temporal scales. In particular, hidden periodicities are often revealed, which may point to teleconnections in the atmosphere-hydrosphere system. As many other analysis methods do, the classical SSA relies on gap free data. Most observational data in the environmental sciences, however, are prone to instrument failure, and do not meet this condition. Here, we investigate extensions to SSA which are designed to fill the gaps, and systematically evaluate their performance. As benchmarks we use artificial time series resembling conventional stochastic processes, and well-known measured runoff time series without missing values, such as the Danube river at Bratislava (daily values from 130 years). In particular, the stability of the estimated covariance matrix, the eigenvalue spectrum, the corresponding reconstructed components and thus the reproducibility of periodic structures either known to exist (for the artificial time series) or assumed to be present (for the measured values) are assessed. In order to evaluate the stability of the method, different temporal patterns of gap occurrences are compared. Among these are randomly distributed, periodic, and single large gaps. A general conclusion is that a single larger gap is more deleterious to structure identification than a set of distributed gaps with the same total length. We demonstrate that the extended SSA is capable to successfully identify and to characterize signal components of hydrological time series with missing values, and conclude that the methodology under investigation is a powerful extension to the statistical toolbox for the environmental scientist.
General questions that arise while investigating hydrological extremes are whether these have dis... more General questions that arise while investigating hydrological extremes are whether these have distinct spatial and temporal variations and how these variations are linked to mean flow conditions. We analyze a large set of European stream flow series. Based on daily observations we derive annual series of stream flow deciles ranging from the minimum to the maximum, resulting in a set
We analyze the behavior of observable quantities of the detailed individual-oriented tree growth ... more We analyze the behavior of observable quantities of the detailed individual-oriented tree growth model TRAGIC++. The model is run on very large time scales (50 kiloyears (kys)) to investigate possible evolutionary processes related to height growth strategies and on small spatial scales (support for approx. 30 adult trees). Transient phases of maximal height and tree number are investigated by means of recurrence quantification analysis (RQA). Simulations are compared with model runs where evolution is excluded. The causes behind phenotype changes in terms of strategy parameters of trees can be identified with the help of RQA, while linear methods alone give ambiguous results. Our investigations suggest that RQA might be a suitable tool for detecting causal relationships in noisy and complex environments.
Introduction Multi-agent competitive games for shared resources may show complex behavior. Despit... more Introduction Multi-agent competitive games for shared resources may show complex behavior. Despite the fact that the set of rules for such a competition is known in principle, the long-term behavior of populations defies analytical treatment. This is partly due to the presence of stationary noise (cf. model description), partly to the fact that the model is spatially rather explicit (tree's architecture is visually recognizable). All global constraints are transformed to local competition for shared resources. Allocation, height growth strategy, biomass production and the like are potentially different from individual to individual. It is hardly conceivable that there could be a shortcut; the only way of investigating the model behavior is by letting it run. Our way of a posteriori analysis is by time series analysis of observable quantities. Here, we investigate recurrence quantification analysis, which is applicable to many types of time series, including relatively
There is an increasing demand for energy from biomass as a substitute to fossil fuels worldwide, ... more There is an increasing demand for energy from biomass as a substitute to fossil fuels worldwide, and the Norwegian government plans to double the production of bioenergy to 9% of the national energy production or to 28 TWh per year by 2020. A large part of this increase may come from forests, which have a great potential with respect to biomass supply as forest growth increasingly has exceeded harvest in the last decades. One feasible option is the utilization of forest residues (needles, twigs and branches) in addition to stems, known as Whole Tree Harvest (WTH). As opposed to WTH, the residues are traditionally left in the forest with Conventional Timber Harvesting (CH). However, the residues contain a large share of the treés nutrients, indicating that WTH may possibly alter the supply of nutrients and organic matter to the soil and the forest ecosystem. This may potentially lead to reduced tree growth. Other implications can be nutrient imbalance, loss of carbon from the soil an...
Our aim is to investigate the temporal dynamics of the “Fraction of Absorbed Photosynthetically A... more Our aim is to investigate the temporal dynamics of the “Fraction of Absorbed Photosynthetically Active Radiation” (fAPAR) on a global scale and its relation to the main meteorological variables across space. We focus on “complex” patterns in time, which are neither regular (trend and seasonality) nor random (noise), but somewhere in bet ween. We quantify complexity and information content or entropy using methods from order statistics and complexity sciences. Time series with high entropy are difficult to predict, whereas time series with high complexity are difficult to describe. This leads to a spatially explicit characterization of complex patterns in a very sensitive way. We use FAPAR observations (SeaWiFS and MERIS, 1998 to 2012) along with gridded global surface air temperature, precipitation and shortwave radiation. All these time series are explored on a pixel–by–pixel basis and clustered according to a very recent classification system of the land surface. In addition, we q...
We report on a series of replicated tracer experiments with deuterium conducted under exceptional... more We report on a series of replicated tracer experiments with deuterium conducted under exceptionally controlled, steady-state storm flow conditions at Gårdsjön in SW Sweden. The Gårdsjön G1 catchment was covered by a roof underneath which natural throughfall was replaced by artificial irrigation with a pre-defined isotopic composition. For four tracer experiments in a subcatchment of G1, deuterium was applied as a narrow pulse so that probability density functions of water transit times could be directly inferred from the observed tracer breakthrough curves. Significantly different water transit times and hence flow paths under similar experimental conditions were observed. Differences were unrelated to both steady-state irrigation and evapotranspiration rates during the experiments.
ABSTRACT Since the advent of the satellite era, global sea-level altimetry data sets are availabl... more ABSTRACT Since the advent of the satellite era, global sea-level altimetry data sets are available. To study complex oceanographic processes and their coupling to atmospheric dynamics it is necessary to advance beyond analyzing global mean sea-level rise or local trends. We apply a wide range of methods from linear and nonlinear time series analysis for investigating the complex dynamics of observed sea-level altimetry time series at different locations around the globe. Employing this toolkit, linear and nonlinear autodependencies (autocorrelation and auto-mutual information functions), deterministic structure (recurrence quantification and recurrence network analysis), time-reversibility characteristics (visibility graph analysis) and the relative importance of stochastic vs. deterministic dynamics (complexity-entropy plane) are studied. Combining the complimentary information from all metrics, consistent spatial patterns of sea-level dynamics are detected. Classical statistical properties such as variance, skewness and Shannon entropy of the probability distribution of sea-level reveal the special importance of western boundary currents as well as parts of the Antarctic Circumpolar Current as regions of particularly complex sea-level dynamics. In turn, the nonlinear dynamics characteristics present a somewhat different pattern exhibiting particularly high complexity in the tropics as well as the Gulf Stream and Kuroshio regions. Notably, these are also the areas where missing values due to atmospheric processes are most prominent. Further research is required to fully disentangle the dynamic complexity of sea-level from potential artifacts in the underlying altimetry data.
ABSTRACT Recent work on sea-level change has mainly focused on long-term trends in the mean. In t... more ABSTRACT Recent work on sea-level change has mainly focused on long-term trends in the mean. In turn, changes in the nonlinear dynamics of sea-level variability have hardly been studied so far, even though they can provide unique information on the ocean's response to long-term changes of different atmospheric driving factors. In this work, we study seven long-term daily tide gauge records from the Baltic Sea with a set of complementary methods of linear and nonlinear time series analysis, including discrete wavelet analysis, autocorrelation-based dimension densities, time- and scale-dependent detrended fluctuation analysis, measures of complexity based on recurrence quantification analysis and recurrence networks, as well as information-theoretic approaches. The linear and nonlinear dynamical properties obtained for different records show consistent long-term variations, which are determined by changes in both local hydrological factors and the regional climatology. Time- and scale-resolved analyses reveal that temporal changes of nonlinear dynamic characteristics affect different temporal scales in different ways and are thus reflected differently by the individual measures evaluated at distinct scales. The corresponding analysis allows identifying and distinguishing long-term changes in sub-annual as well as annual to decadal-scale variability, which can be related to triggering factors acting at different temporal scales. In general, the results of all applied analyses display a consistent spatial pattern with a marked latitudinal complexity gradient, with sea-level variability being most complex close to the Baltic entrance and least complex in the central Baltic Sea.
Stream flow observations from a geographical region are known to often exhibit strong common beha... more Stream flow observations from a geographical region are known to often exhibit strong common behavior. In order to assess the temporal evolution of the complexity of stream flow time series from all over Europe, we employ the recently developed Linear Variance Decay dimension density (^LV D). It is estimated as the parameter of an exponential decay function fitted to the
Singular System Analysis (SSA) is a powerful data-oriented time series decomposition tool used e.... more Singular System Analysis (SSA) is a powerful data-oriented time series decomposition tool used e.g. in atmospheric physics and hydrology to extract the dynamics contained in time series at arbitrary temporal scales. In particular, hidden periodicities are often revealed, which may point to teleconnections in the atmosphere-hydrosphere system. As many other analysis methods do, the classical SSA relies on gap free data. Most observational data in the environmental sciences, however, are prone to instrument failure, and do not meet this condition. Here, we investigate extensions to SSA which are designed to fill the gaps, and systematically evaluate their performance. As benchmarks we use artificial time series resembling conventional stochastic processes, and well-known measured runoff time series without missing values, such as the Danube river at Bratislava (daily values from 130 years). In particular, the stability of the estimated covariance matrix, the eigenvalue spectrum, the corresponding reconstructed components and thus the reproducibility of periodic structures either known to exist (for the artificial time series) or assumed to be present (for the measured values) are assessed. In order to evaluate the stability of the method, different temporal patterns of gap occurrences are compared. Among these are randomly distributed, periodic, and single large gaps. A general conclusion is that a single larger gap is more deleterious to structure identification than a set of distributed gaps with the same total length. We demonstrate that the extended SSA is capable to successfully identify and to characterize signal components of hydrological time series with missing values, and conclude that the methodology under investigation is a powerful extension to the statistical toolbox for the environmental scientist.
General questions that arise while investigating hydrological extremes are whether these have dis... more General questions that arise while investigating hydrological extremes are whether these have distinct spatial and temporal variations and how these variations are linked to mean flow conditions. We analyze a large set of European stream flow series. Based on daily observations we derive annual series of stream flow deciles ranging from the minimum to the maximum, resulting in a set
We analyze the behavior of observable quantities of the detailed individual-oriented tree growth ... more We analyze the behavior of observable quantities of the detailed individual-oriented tree growth model TRAGIC++. The model is run on very large time scales (50 kiloyears (kys)) to investigate possible evolutionary processes related to height growth strategies and on small spatial scales (support for approx. 30 adult trees). Transient phases of maximal height and tree number are investigated by means of recurrence quantification analysis (RQA). Simulations are compared with model runs where evolution is excluded. The causes behind phenotype changes in terms of strategy parameters of trees can be identified with the help of RQA, while linear methods alone give ambiguous results. Our investigations suggest that RQA might be a suitable tool for detecting causal relationships in noisy and complex environments.
Introduction Multi-agent competitive games for shared resources may show complex behavior. Despit... more Introduction Multi-agent competitive games for shared resources may show complex behavior. Despite the fact that the set of rules for such a competition is known in principle, the long-term behavior of populations defies analytical treatment. This is partly due to the presence of stationary noise (cf. model description), partly to the fact that the model is spatially rather explicit (tree's architecture is visually recognizable). All global constraints are transformed to local competition for shared resources. Allocation, height growth strategy, biomass production and the like are potentially different from individual to individual. It is hardly conceivable that there could be a shortcut; the only way of investigating the model behavior is by letting it run. Our way of a posteriori analysis is by time series analysis of observable quantities. Here, we investigate recurrence quantification analysis, which is applicable to many types of time series, including relatively
There is an increasing demand for energy from biomass as a substitute to fossil fuels worldwide, ... more There is an increasing demand for energy from biomass as a substitute to fossil fuels worldwide, and the Norwegian government plans to double the production of bioenergy to 9% of the national energy production or to 28 TWh per year by 2020. A large part of this increase may come from forests, which have a great potential with respect to biomass supply as forest growth increasingly has exceeded harvest in the last decades. One feasible option is the utilization of forest residues (needles, twigs and branches) in addition to stems, known as Whole Tree Harvest (WTH). As opposed to WTH, the residues are traditionally left in the forest with Conventional Timber Harvesting (CH). However, the residues contain a large share of the treés nutrients, indicating that WTH may possibly alter the supply of nutrients and organic matter to the soil and the forest ecosystem. This may potentially lead to reduced tree growth. Other implications can be nutrient imbalance, loss of carbon from the soil an...
Our aim is to investigate the temporal dynamics of the “Fraction of Absorbed Photosynthetically A... more Our aim is to investigate the temporal dynamics of the “Fraction of Absorbed Photosynthetically Active Radiation” (fAPAR) on a global scale and its relation to the main meteorological variables across space. We focus on “complex” patterns in time, which are neither regular (trend and seasonality) nor random (noise), but somewhere in bet ween. We quantify complexity and information content or entropy using methods from order statistics and complexity sciences. Time series with high entropy are difficult to predict, whereas time series with high complexity are difficult to describe. This leads to a spatially explicit characterization of complex patterns in a very sensitive way. We use FAPAR observations (SeaWiFS and MERIS, 1998 to 2012) along with gridded global surface air temperature, precipitation and shortwave radiation. All these time series are explored on a pixel–by–pixel basis and clustered according to a very recent classification system of the land surface. In addition, we q...
We report on a series of replicated tracer experiments with deuterium conducted under exceptional... more We report on a series of replicated tracer experiments with deuterium conducted under exceptionally controlled, steady-state storm flow conditions at Gårdsjön in SW Sweden. The Gårdsjön G1 catchment was covered by a roof underneath which natural throughfall was replaced by artificial irrigation with a pre-defined isotopic composition. For four tracer experiments in a subcatchment of G1, deuterium was applied as a narrow pulse so that probability density functions of water transit times could be directly inferred from the observed tracer breakthrough curves. Significantly different water transit times and hence flow paths under similar experimental conditions were observed. Differences were unrelated to both steady-state irrigation and evapotranspiration rates during the experiments.
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Papers by Holger Lange