David Kleinhans

Integration of Renewable Energy Sources in Future Power Systems: The Role of Storage

Integrating a high share of electricity from non-dispatchable Renewable Energy Sources in a power supply system is a challenging task. One option considered in many studies dealing with prospective power systems is the installation of storage devices to balance the fluctuations in power production. However, it is not yet clear how soon storage devices will be needed and how the integration process depends on different storage parameters. Using long-term solar and wind energy power production data series, we present a modelling approach to investigate the influence of storage size and efficiency on the pathway towards a 100% RES scenario. Applying our approach to data for Germany, we found that up to 50% of the overall electricity demand can be met by an optimum combination of wind and solar resources without both curtailment and storage devices if the remaining energy is provided by sufficiently flexible power plants. Our findings show further that the installation of small, but highly efficient storage devices is already highly beneficial for the RES integration, while seasonal storage devices are only needed when more than 80% of the electricity demand can be met by wind and solar energy. Our results imply that a compromise between the installation of additional generation capacities and storage capacities is required.

Directional genetic differentiation and relative migration

Abstract Understanding the population structure and patterns of gene flow within species is of fundamental importance to the study of evolution. In the fields of population and evolutionary genetics, measures of genetic differentiation are commonly used to gather this information. One potential caveat is that these measures assume gene flow to be symmetric. However, asymmetric gene flow is common in nature, especially in systems driven by physical processes such as wind or water currents. As information about levels of asymmetric gene flow among populations is essential for the correct interpretation of the distribution of contemporary genetic diversity within species, this should not be overlooked. To obtain information on asymmetric migration patterns from genetic data, complex models based on maximum‐likelihood or Bayesian approaches generally need to be employed, often at great computational cost. Here, a new simpler and more efficient approach for understanding gene flow patterns is presented. This approach allows the estimation of directional components of genetic divergence between pairs of populations at low computational effort, using any of the classical or modern measures of genetic differentiation. These directional measures of genetic differentiation can further be used to calculate directional relative migration and to detect asymmetries in gene flow patterns. This can be done in a user‐friendly web application called divMigrate‐online introduced in this study. Using simulated data sets with known gene flow regimes, we demonstrate that the method is capable of resolving complex migration patterns under a range of study designs.

Reconstruction of Complex Dynamical Systems Affected by Strong Measurement Noise

This Letter reports on a new approach to properly analyze time series of dynamical systems which are spoilt by the simultaneous presence of dynamical noise and measurement noise. It is shown that even strong external measurement noise as well as dynamical noise which is an intrinsic part of the dynamical process can be quantified correctly, solely on the basis of measured time series and proper data analysis. Finally, real world data sets are presented pointing out the relevance of the new approach.

Seascape analysis reveals regional gene flow patterns among populations of a marine planktonic diatom

We investigated the gene flow of the common marine diatom, Skeletonema marinoi, in Scandinavian waters and tested the null hypothesis of panmixia. Sediment samples were collected from the Danish Straits, Kattegat and Skagerrak. Individual strains were established from germinated resting stages. A total of 350 individuals were genotyped by eight microsatellite markers. Conventional F-statistics showed significant differentiation between the samples. We therefore investigated whether the genetic structure could be explained using genetic models based on isolation by distance (IBD) or by oceanographic connectivity. Patterns of oceanographic circulation are seasonally dependent and therefore we estimated how well local oceanographic connectivity explains gene flow month by month. We found no significant relationship between genetic differentiation and geographical distance. Instead, the genetic structure of this dominant marine primary producer is best explained by local oceanographic connectivity promoting gene flow in a primarily south to north direction throughout the year. Oceanographic data were consistent with the significant FST values between several pairs of samples. Because even a small amount of genetic exchange prevents the accumulation of genetic differences in F-statistics, we hypothesize that local retention at each sample site, possibly as resting stages, is an important component in explaining the observed genetic structure.

Maximum likelihood estimation of drift and diffusion functions

The maximum likelihood approach is adapted to the problem of estimation of drift and diffusion functions of stochastic processes from measured time series. We reconcile a previously devised iterative procedure [Kleinhans et al., Physics Letters A (346), 2005] and put the application of the method on a firm theoretical basis.

Improved estimation of Fokker-Planck equations through optimization.

An improved method for the description of hierarchical complex systems by means of a Fokker-Planck equation is presented. In particular the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm for constraint problems is used to minimize the distance between the numerical solutions of the Fokker-Planck equation and the empirical probability density functions and thus to estimate properly the drift and diffusion term of the Fokker-Planck equation. The optimization routine is applied to a time series of velocity measurements obtained from a turbulent helium gas jet in order to demonstrate the benefits and to quantify the improvements of this optimization routine.

On the impact of dispersal asymmetry on metapopulation persistence

Metapopulation theory for a long time has assumed dispersal to be symmetric, i.e. patches are connected through migrants dispersing bi-directionally without a preferred direction. However, for natural populations symmetry is often broken, e.g. for species in the marine environment dispersing through the transport of pelagic larvae with ocean currents. The few recent studies of asymmetric dispersal concluded that asymmetry has a distinct negative impact on the persistence of metapopulations. Detailed analysis, however, revealed that these previous studies might have been unable to properly disentangle the effect of symmetry from other potentially confounding properties of dispersal patterns. We resolve this issue by systematically investigating the symmetry of dispersal patterns and its impact on metapopulation persistence. Our main analysis based on a metapopulation model equivalent to previous studies but now applied on regular dispersal patterns aims to isolate the effect of dispersal symmetry on metapopulation persistence. Our results suggest that asymmetry in itself does not imply negative effects on metapopulation persistence. For this reason we recommend to investigate it in connection with other properties of dispersal instead of in isolation.

Extracting strong measurement noise from stochastic time series: applications to empirical data.

It is a big challenge in the analysis of experimental data to disentangle the unavoidable measurement noise from the intrinsic dynamical noise. Here we present a general operational method to extract measurement noise from stochastic time series even in the case when the amplitudes of measurement noise and uncontaminated signal are of the same order of magnitude. Our approach is based on a recently developed method for a nonparametric reconstruction of Langevin processes. Minimizing a proper non-negative function, the procedure is able to correctly extract strong measurement noise and to estimate drift and diffusion coefficients in the Langevin equation describing the evolution of the original uncorrupted signal. As input, the algorithm uses only the two first conditional moments extracted directly from the stochastic series and is therefore suitable for a broad panoply of different signals. To demonstrate the power of the method, we apply the algorithm to synthetic as well as climatological measurement data, namely, the daily North Atlantic Oscillation index, shedding light on the discussion of the nature of its underlying physical processes.

Estimation of drift and diffusion functions from time series data: a maximum likelihood framework.

Complex systems are characterized by a huge number of degrees of freedom often interacting in a nonlinear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic dynamics in time. Recently, techniques for the estimation of the corresponding stochastic differential equations from measured data have been introduced. This paper develops a framework for the estimation of the functions and their respective (Bayesian posterior) confidence regions based on likelihood estimators. In succession, approximations are introduced that significantly improve the efficiency of the estimation procedure. While being consistent with standard approaches to the problem, this paper solves important problems concerning the applicability and the accuracy of estimated parameters.

Principal axes for stochastic dynamics

We introduce a general procedure for directly ascertaining how many independent stochastic sources exist in a complex system modeled through a set of coupled Langevin equations of arbitrary dimension. The procedure is based on the computation of the eigenvalues and the corresponding eigenvectors of local diffusion matrices. We demonstrate our algorithm by applying it to two examples of systems showing Hopf bifurcation. We argue that computing the eigenvectors associated to the eigenvalues of the diffusion matrix at local mesh points in the phase space enables one to define vector fields of stochastic eigendirections. In particular, the eigenvector associated to the lowest eigenvalue defines the path of minimum stochastic forcing in phase space, and a transform to a new coordinate system aligned with the eigenvectors can increase the predictability of the system.