Estimating causal networks in biosphere–atmosphere interaction with the PCMCI approach

Local meteorological conditions and biospheric activity are tightly coupled. Understanding these links is an essential prerequisite for predicting the Earth system under climate change conditions. However, many empirical studies on the interaction between the biosphere and the atmosphere are based on correlative approaches that are not able to deduce causal paths, and only very few studies apply causal discovery methods. Here, we use a recently proposed causal graph discovery algorithm, which aims to reconstruct the causal dependency structure underlying a set of time series. We explore the potential of this method to infer temporal dependencies in biosphere-atmosphere interactions. Specifically we address the following questions: How do periodicity and heteroscedasticity influence causal detection rates, i.e. the detection of existing and non-existing links? How consistent are results for noise-contaminated data? Do results exhibit an increased information content that justifies the use of this causal-inference method? We explore the first question using artificial time series with well known dependencies that mimic real-world biosphere-atmosphere interactions. The two remaining questions are addressed jointly in two case studies utilizing observational data. Firstly, we analyse three replicated eddy covariance datasets from a Mediterranean ecosystem at half hourly time resolution allowing us to understand the impact of measurement uncertainties. Secondly, we analyse global NDVI time series (GIMMS 3g) along with gridded climate data to study large-scale climatic drivers of vegetation greenness. Overall, the results confirm the capacity of the causal discovery method to extract time-lagged linear dependencies under realistic settings. The violation of the method's assumptions increases the likelihood to detect false links. Nevertheless, we consistently identify interaction patterns in observational data. Our findings suggest that estimating a directed biosphere-atmosphere network at the ecosystem level can offer novel possibilities to unravel complex multi-directional interactions. Other than classical correlative approaches, our findings are constrained to a few meaningful set of relations which can be powerful insights for the evaluation of terrestrial ecosystem models

Bead, Hoop, and Spring as a Classical Spontaneous Symmetry Breaking Problem

We describe a simple mechanical system that involves Spontaneous Symmetry Breaking. The system consists of two beads constrained to slide along a hoop and attached each other through a spring. When the hoop rotates about a fixed axis, the spring-beads system will change its equilibrium position as a function of the angular velocity. The system shows two different regions of symmetry separated by a critical point analogous to a second order transition. The competitive balance between the rotational diynamics and the interaction of the spring causes an Spontaneous Symmetry Breaking just as the balance between temperature and the spin interaction causes a transition in a ferromagnetic system. In addition, the gravitational potential act as an external force that causes explicit symmetry breaking and a feature of first-order transition. Near the transition point, the system exhibits a universal critical behavior where the changes of the parameter of order is described by the critical exponent beta =1/2 and the susceptibility by gamma =1. We also found a chaotic behavior near the critical point. Through a demostrative device we perform some qualitative observations that describe important features of the system.Comment: 7 pages, 2 tables, 30 figures, LaTeX2

Quantum Phase Transition and Berry Phase in an Extended Dicke Model

We investigate quantum phase transitions, quantum criticality, and Berry phase for the ground state of an ensemble of non-interacting two-level atoms embedded in a non-linear optical medium, coupled to a single-mode quantized electromagnetic field. The optical medium is pumped externally through a classical electric field, so that there is a degenerate parametric amplification effect, which strongly modifies the field dynamics without affecting the atomic sector. Through a semiclassical description the different phases of this extended Dicke model are described. The quantum phase transition is characterized with the expectation values of some observables of the system as well as the Berry phase and its first derivative, where such quantities serve as order parameters. It is remarkable that the model allows the control of the quantum criticality through a suitable choice of the parameters of the non-linear optical medium, which could make possible the use of a low intensity laser to access the superradiant region experimentally.Comment: 7 pages, 4 figures, submitted to The European Physical Journal

Isogeometric analysis of hyperelastic materials using petiGA

In this work different nonlinear hyperelastic models for slightly compressible materials are implemented in an isogeometric finite element model. This is done within the recently developed computational framework called PetIGA, which uses isogeometric analysis and modern computational tools to solve systems of equations directly and iteratively. A flexible theoretical background is described to implement other hyperelastic models and possibly transient problems in future work. Results show quadratic convergence of the nonlinear solution consistent with the Newton-Raphson method that was used. Finally, PetIGA proves to be a powerful and versatile tool to solve these types of problems efficiently. © 2013 The Authors. Published by Elsevier B.V

Extreme events in gross primary production: a characterization across continents

Climate extremes can affect the functioning of terrestrial ecosystems, for instance via a reduction of the photosynthetic capacity or alterations of respiratory processes. Yet the dominant regional and seasonal effects of hydrometeorological extremes are still not well documented and in the focus of this paper. Specifically, we quantify and characterize the role of large spatiotemporal extreme events in gross primary production (GPP) as triggers of continental anomalies. We also investigate seasonal dynamics of extreme impacts on continental GPP anomalies. We find that the 50 largest positive extremes (i.e., statistically unusual increases in carbon uptake rates) and negative extremes (i.e., statistically unusual decreases in carbon uptake rates) on each continent can explain most of the continental variation in GPP, which is in line with previous results obtained at the global scale. We show that negative extremes are larger than positive ones and demonstrate that this asymmetry is particularly strong in South America and Europe. Our analysis indicates that the overall impacts and the spatial extents of GPP extremes are power-law distributed with exponents that vary little across continents. Moreover, we show that on all continents and for all data sets the spatial extents play a more important role for the overall impact of GPP extremes compared to the durations or maximal GPP. An analysis of possible causes across continents indicates that most negative extremes in GPP can be attributed clearly to water scarcity, whereas extreme temperatures play a secondary role. However, for Europe, South America and Oceania we also identify fire as an important driver. Our findings are consistent with remote sensing products. An independent validation against a literature survey on specific extreme events supports our results to a large extent

Femtosecond pulses and dynamics of molecular photoexcitation: RbCs example

We investigate the dynamics of molecular photoexcitation by unchirped femtosecond laser pulses using RbCs as a model system. This study is motivated by a goal of optimizing a two-color scheme of transferring vibrationally-excited ultracold molecules to their absolute ground state. In this scheme the molecules are initially produced by photoassociation or magnetoassociation in bound vibrational levels close to the first dissociation threshold. We analyze here the first step of the two-color path as a function of pulse intensity from the low-field to the high-field regime. We use two different approaches, a global one, the 'Wavepacket' method, and a restricted one, the 'Level by Level' method where the number of vibrational levels is limited to a small subset. The comparison between the results of the two approaches allows one to gain qualitative insights into the complex dynamics of the high-field regime. In particular, we emphasize the non-trivial and important role of far-from-resonance levels which are adiabatically excited through 'vertical' transitions with a large Franck-Condon factor. We also point out spectacular excitation blockade due to the presence of a quasi-degenerate level in the lower electronic state. We conclude that selective transfer with femtosecond pulses is possible in the low-field regime only. Finally, we extend our single-pulse analysis and examine population transfer induced by coherent trains of low-intensity femtosecond pulses.Comment: 25 pages, 12 figure

Kernel Methods and their derivatives: Concept and perspectives for the Earth system sciences

Kernel methods are powerful machine learning techniques which implement generic non-linear functions to solve complex tasks in a simple way. They Have a solid mathematical background and exhibit excellent performance in practice. However, kernel machines are still considered black-box models as the feature mapping is not directly accessible and difficult to interpret.The aim of this work is to show that it is indeed possible to interpret the functions learned by various kernel methods is intuitive despite their complexity. Specifically, we show that derivatives of these functions have a simple mathematical formulation, are easy to compute, and can be applied to many different problems. We note that model function derivatives in kernel machines is proportional to the kernel function derivative. We provide the explicit analytic form of the first and second derivatives of the most common kernel functions with regard to the inputs as well as generic formulas to compute higher order derivatives. We use them to analyze the most used supervised and unsupervised kernel learning methods: Gaussian Processes for regression, Support Vector Machines for classification, Kernel Entropy Component Analysis for density estimation, and the Hilbert-Schmidt Independence Criterion for estimating the dependency between random variables. For all cases we expressed the derivative of the learned function as a linear combination of the kernel function derivative. Moreover we provide intuitive explanations through illustrative toy examples and show how to improve the interpretation of real applications in the context of spatiotemporal Earth system data cubes. This work reflects on the observation that function derivatives may play a crucial role in kernel methods analysis and understanding.Comment: 21 pages, 10 figures, PLOS One Journa