Low-Dimensional Representations of Earth System Processes

In times of global change, we must closely monitor the state of our planet in order to understand gradual or abrupt changes early on. In fact, each of the Earth's subsystems-i.e. the biosphere, atmosphere, hydrosphere, cryosphere, and anthroposphere-can be analyzed from a multitude of data streams. However, since it is very hard to jointly interpret multiple monitoring data streams in parallel, one often aims for some summarizing indicator. Climate indices, for example, summarize the state of atmospheric circulation in a region, e.g. the Multivariate ENSO (El Ñino-Southern Oscillation) Index. Indicator approaches have been used extensively to describe socioeconomic data too, and a range of indices have been proposed to synthesize and interpret this information. For instance the "Human Development Index" (HDI) by the United Nations Development Programme was designed to capture specific aspects of development. "Dimensionality reduction" (DR) is a widely used approach to find low dimensional and interpretable representations of data that are natively embedded in high-dimensional spaces. Here, we propose a robust method to create indicators using dimensionality reduction to better represent the terrestrial biosphere and the global socioeconomic system. We aim to explore the performance of the approach and to interpret the resulting indicators. For biosphere indicators, the concept was tested using 12 explanatory variables representing the biophysical states of ecosystems and land-atmosphere water, energy, and carbon fluxes. We find that two indicators account for 73% of the variance of the state of the biosphere in space and time. While the first indicator summarizes productivity patterns, the second indicator summarizes variables representing water and energy availability. Anomalies in the indicators clearly identify extreme events, such as the Amazon droughts (2005 and 2010) and the Russian heatwave (2010), they also allow us to interpret the impacts of these events. The indicators also reveal changes in the seasonal cycle, e.g. increasing seasonal amplitudes of productivity in agricultural areas and in arctic regions. We also apply the method on the "World Development Indicators", a database with more than 1500 variables, to track the socioeconomic development at a country level. The aim was to extract the core dimensions of development in a highly efficient way, using a method of nonlinear dimensionality reduction. We find that over 90% of variance in the WDIs can be represented by five uncorrelated and nonlinear dimensions. The first dimension (explaining 74%) represents the state of education, health, income, infrastructure, trade, population, and pollution. The second dimension (explaining 10%) differentiates countries by gender ratios, labor market, and energy production patterns. Overall, we find that the data contained in the WDIs are highly nonlinear therefore requiring nonlinear methods to extract the main patterns of development. Globally, most countries show rather consistent temporal trends towards wealthier and aging societies. Deviations from the long-term trajectories are detected with our approach during warfare, environmental disasters, or fundamental political changes. In general we find that the indicator approach is able to extract general patterns from complex databases and that it can be applied to databases of varying characteristics. We also find that indicators are can different kinds of changes occurring in the system, such as extreme events, permanent changes or trends. Therefore it is a useful tool for general monitoring and exploratory data analysis. The approach is flexible and can be applied to complex datasets, such as large data, nonlinear data, as well as data with many missing values.In times of global change, we must closely monitor the state of our planet in order to understand gradual or abrupt changes early on. In fact, each of the Earth's subsystems-i.e. the biosphere, atmosphere, hydrosphere, cryosphere, and anthroposphere-can be analyzed from a multitude of data streams. However, since it is very hard to jointly interpret multiple monitoring data streams in parallel, one often aims for some summarizing indicator. Climate indices, for example, summarize the state of atmospheric circulation in a region, e.g. the Multivariate ENSO (El Ñino-Southern Oscillation) Index. Indicator approaches have been used extensively to describe socioeconomic data too, and a range of indices have been proposed to synthesize and interpret this information. For instance the "Human Development Index" (HDI) by the United Nations Development Programme was designed to capture specific aspects of development. "Dimensionality reduction" (DR) is a widely used approach to find low dimensional and interpretable representations of data that are natively embedded in high-dimensional spaces. Here, we propose a robust method to create indicators using dimensionality reduction to better represent the terrestrial biosphere and the global socioeconomic system. We aim to explore the performance of the approach and to interpret the resulting indicators. For biosphere indicators, the concept was tested using 12 explanatory variables representing the biophysical states of ecosystems and land-atmosphere water, energy, and carbon fluxes. We find that two indicators account for 73% of the variance of the state of the biosphere in space and time. While the first indicator summarizes productivity patterns, the second indicator summarizes variables representing water and energy availability. Anomalies in the indicators clearly identify extreme events, such as the Amazon droughts (2005 and 2010) and the Russian heatwave (2010), they also allow us to interpret the impacts of these events. The indicators also reveal changes in the seasonal cycle, e.g. increasing seasonal amplitudes of productivity in agricultural areas and in arctic regions. We also apply the method on the "World Development Indicators", a database with more than 1500 variables, to track the socioeconomic development at a country level. The aim was to extract the core dimensions of development in a highly efficient way, using a method of nonlinear dimensionality reduction. We find that over 90% of variance in the WDIs can be represented by five uncorrelated and nonlinear dimensions. The first dimension (explaining 74%) represents the state of education, health, income, infrastructure, trade, population, and pollution. The second dimension (explaining 10%) differentiates countries by gender ratios, labor market, and energy production patterns. Overall, we find that the data contained in the WDIs are highly nonlinear therefore requiring nonlinear methods to extract the main patterns of development. Globally, most countries show rather consistent temporal trends towards wealthier and aging societies. Deviations from the long-term trajectories are detected with our approach during warfare, environmental disasters, or fundamental political changes. In general we find that the indicator approach is able to extract general patterns from complex databases and that it can be applied to databases of varying characteristics. We also find that indicators are can different kinds of changes occurring in the system, such as extreme events, permanent changes or trends. Therefore it is a useful tool for general monitoring and exploratory data analysis. The approach is flexible and can be applied to complex datasets, such as large data, nonlinear data, as well as data with many missing values

Quantum dark solitons in Bose gas confined in a hard wall box

Schr\"odinger equation for Bose gas with repulsive contact interactions in one-dimensional space may be solved analytically with the help of the Bethe ansatz if we impose periodic boundary conditions. It was shown that in such a system there exist many-body eigenstates directly corresponding to dark soliton solutions of the mean-field equation. The system is still integrable if one switches from the periodic boundary conditions to an infinite square well potential. The corresponding eigenstates were constructed by M. Gaudin. We analyze weak interaction limit of Gaudin's solutions and identify parametrization of eigenstates strictly connected with single and multiple dark solitons. Numerical simulations of detection of particle's positions reveal dark solitons in the weak interaction regime and their quantum nature in the presence of strong interactions.Comment: 7 pages, 4 figures, version accepted for publication in Phys. Rev.

Crowd-sourced plant occurrence data provide a reliable description of macroecological gradients

Deep learning algorithms classify plant species with high accuracy, and smartphone applications leverage this technology to enable users to identify plant species in the field. The question we address here is whether such crowd-sourced data contain substantial macroecological information. In particular, we aim to understand if we can detect known environmental gradients shaping plant co-occurrences. In this study we analysed 1 million data points collected through the use of the mobile app Flora Incognita between 2018 and 2019 in Germany and compared them with Florkart, containing plant occurrence data collected by more than 5000 floristic experts over a 70-year period. The direct comparison of the two data sets reveals that the crowd-sourced data particularly undersample areas of low population density. However, using nonlinear dimensionality reduction we were able to uncover macroecological patterns in both data sets that correspond well to each other. Mean annual temperature, temperature seasonality and wind dynamics as well as soil water content and soil texture represent the most important gradients shaping species composition in both data collections. Our analysis describes one way of how automated species identification could soon enable near real-time monitoring of macroecological patterns and their changes, but also discusses biases that must be carefully considered before crowd-sourced biodiversity data can effectively guide conservation measures

A Deep Chandra ACIS Study of NGC 4151. III. the Line Emission and Spectral Analysis of the Ionization Cone

This paper is the third in a series in which we present deep Chandra ACIS-S imaging spectroscopy of the Seyfert 1 galaxy NGC 4151, devoted to study its complex circum-nuclear X-ray emission. Emission features in the soft X-ray spectrum of the bright extended emission (L[0.3-2keV]~10^40 erg/s) at r>130 pc (2") are consistent with the brighter OVII, OVIII, and NeIX lines seen in the Chandra HETGS and XMM-Newton RGS spectra below 2 keV. We construct emission line images of these features and find good morphological correlations with the narrow line region clouds mapped in [OIII]5007A. Self-consistent photoionization models provide good descriptions of the spectra of the large scale emission, as well as resolved structures, supporting the dominant role of nuclear photoionization, although displacement of optical and X-ray features implies a more complex medium. Collisionally ionized emission is estimated to be <12% of the extended emission. Presence of both low and high ionization spectral components and extended emission in the X-ray image perpendicular to the bicone indicates leakage of nuclear ionization, likely filtered through warm absorbers, instead of being blocked by a continuous obscuring torus. The ratios of [OIII]/soft X-ray flux are approximately constant (~15) for the 1.5 kpc radius spanned by these measurements, indicating a relatively constant ionization parameter, consistent with the photoionized outflow of a wind-like density profile. Using spatially resolved features, we estimate that the mass outflow rate in NGC 4151 is ~2Msun/yr at 130 pc and the kinematic power of the ionized outflow is 1.7x10^41 erg/s, approximately 0.3% of the bolometric luminosity of NGC 4151.Comment: 45 pages. 18 figures. Accepted to Ap

Imputing missing data in plant traits: A guide to improve gap‐filling

Aim: Globally distributed plant trait data are increasingly used to understand relationships between biodiversity and ecosystem processes. However, global trait databases are sparse because they are compiled from many, mostly small databases. This sparsity in both trait space completeness and geographical distribution limits the potential for both multivariate and global analyses. Thus, ‘gap-filling’ approaches are often used to impute missing trait data. Recent methods, like Bayesian hierarchical probabilistic matrix factorization (BHPMF), can impute large and sparse data sets using side information. We investigate whether BHPMF imputation leads to biases in trait space and identify aspects influencing bias to provide guidance for its usage. Innovation: We use a fully observed trait data set from which entries are randomly removed, along with extensive but sparse additional data. We use BHPMF for imputation and evaluate bias by: (1) accuracy (residuals, RMSE, trait means), (2) correlations (bi-and multivariate) and (3) taxonomic and functional clustering (valuewise, uni-and multivariate). BHPMF preserves general patterns of trait distributions but induces taxonomic clustering. Data set–external trait data had little effect on induced taxonomic clustering and stabilized trait–trait correlations. Main Conclusions: Our study extends the criteria for the evaluation of gap-filling beyond RMSE, providing insight into statistical data structure and allowing better informed use of imputed trait data, with improved practice for imputation. We expect our findings to be valuable beyond applications in plant ecology, for any study using hierarchical side information for imputation

A Multiwavelength Study of Young Massive Star-Forming Regions. III. Mid-Infrared Emission

We present mid-infrared (MIR) observations, made with the TIMMI2 camera on the ESO 3.6 m telescope, toward 14 young massive star-forming regions. All regions were imaged in the N band, and nine in the Q band, with an angular resolution of ~ 1 arcsec. Typically, the regions exhibit a single or two compact sources (with sizes in the range 0.008-0.18 pc) plus extended diffuse emission. The Spitzer-Galactic Legacy Infrared Mid-Plane Survey Extraordinaire images of these regions show much more extended emission than that seen by TIMMI2, and this is attributed to polycyclic aromatic hydrocarbon (PAH) bands. For the MIR sources associated with radio continuum radiation (Paper I) there is a close morphological correspondence between the two emissions, suggesting that the ionized gas (radio source) and hot dust (MIR source) coexist inside the H II region. We found five MIR compact sources which are not associated with radio continuum emission, and are thus prime candidates for hosting young massive protostars. In particular, objects IRAS 14593-5852 II (only detected at 17.7 microns) and 17008-4040 I are likely to be genuine O-type protostellar objects. We also present TIMMI2 N-band spectra of eight sources, all of which are dominated by a prominent silicate absorption feature (~ 9.7 microns). From these data we estimate column densities in the range (7-17)x10^22 cm^-2, in good agreement with those derived from the 1.2 mm data (Paper II). Seven sources show bright [Ne II] line emission, as expected from ionized gas regions. Only IRAS 123830-6128 shows detectable PAH emission at 8.6 and 11.3 microns.Comment: Published in ApJ. 15 pages, 6 figures. Formatted with emulateapj; v2: Minor language changes to match the published versio

A Deep Chandra ACIS Study of NGC 4151. II. The Innermost Emission Line Region and Strong Evidence for Radio Jet-NLR Cloud Collision

We have studied the X-ray emission within the inner 150 pc radius of NGC 4151 by constructing high spatial resolution emission line images of OVII, OVIII, and NeIX. These maps show extended structures that are spatially correlated with the radio outflow and optical [OIII] emission. We find strong evidence for jet--gas cloud interaction, including morphological correspondences with regions of X-ray enhancement, peaks of near-infrared [FeII] emission, and optical clouds. In these regions, moreover, we find evidence of elevated NeIX/OVII ratios; the X-ray emission of these regions also exceeds that expected from nuclear photoionization. Spectral fitting reveals the presence of a collisionally ionized component. The thermal energy of the hot gas suggests that >0.1% of the estimated jet power is deposited into the host interstellar medium through interaction between the radio jet and the dense medium of the circum-nuclear region. We find possible pressure equilibrium between the collisionally ionized hot gas and the photoionized line-emitting cool clouds. We also obtain constraints on the extended iron and silicon fluorescent emission. Both lines are spatially unresolved. The upper limit on the contribution of an extended emission region to the Fe Kalpha emission is <5% of the total, in disagreement with a previous claim that 65% of the Fe Kalpha emission originates in the extended narrow line region.Comment: Accepted for publication in ApJ. 28 pages, 9 figure

A Deep Chandra ACIS Study of NGC 4151. I. the X-ray Morphology of the 3 kpc-diameter Circum-nuclear Region and Relation to the Cold Interstellar Medium

We report on the imaging analysis of 200 ks sub-arcsecond resolution Chandra ACIS-S observations of the nearby Seyfert 1 galaxy NGC 4151. Bright, structured soft X-ray emission is observed to extend from 30 pc to 1.3 kpc in the south-west from the nucleus, much farther than seen in earlier X-ray studies. The terminus of the north-eastern X-ray emission is spatially coincident with a CO gas lane, where the outflow likely encounters dense gas in the host galactic disk. X-ray emission is also detected outside the boundaries of the ionization cone, which indicates that the gas there is not completely shielded from the nuclear continuum, as would be the case for a molecular torus collimating the bicone. In the central r<200 pc region, the subpixel processing of the ACIS data recovers the morphological details on scales of <30~pc (<0.5") first discovered in Chandra HRC images. The X-ray emission is more absorbed towards the boundaries of the ionization cone, as well as perpendicular to the bicone along the direction of a putative torus in NGC 4151. The innermost region where X-ray emission shows the highest hardness ratio, is spatially coincident with the near-infrared resolved H_2 emission and dusty spirals we find in an HST V-H color image. The agreement between the observed H_2 line flux and the value predicted from X-ray-irradiated molecular cloud models supports photo-excitation by X-rays from the active nucleus as the origin of the H_2 line, although contribution from UV fluorescence or collisional excitation cannot be fully ruled out with current data. The discrepancy between the mass of cold molecular gas inferred from recent CO and near-infrared H_2 observations may be explained by the anomalous CO abundance in this X-ray dominated region. The total H_2 mass derived from the X-ray observation agrees with measurement in Storchi-Bergmann et al.Comment: 33 pages, 9 figures and 2 table

Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons

One of the most remarkable results of quantum mechanics is the fact that many-body quantum systems may exhibit phase transitions even at zero temperature. Quantum fluctuations, deeply rooted in Heisenberg's uncertainty principle, and not thermal fluctuations, drive the system from one phase to another. Typically, the relative strength of two competing terms in the system's Hamiltonian is changed across a finite critical value. A well-known example is the Mott-Hubbard quantum phase transition from a superfluid to an insulating phase, which has been observed for weakly interacting bosonic atomic gases. However, for strongly interacting quantum systems confined to lower-dimensional geometry a novel type of quantum phase transition may be induced for which an arbitrarily weak perturbation to the Hamiltonian is sufficient to drive the transition. Here, for a one-dimensional (1D) quantum gas of bosonic caesium atoms with tunable interactions, we observe the commensurate-incommensurate quantum phase transition from a superfluid Luttinger liquid to a Mott-insulator. For sufficiently strong interactions, the transition is induced by adding an arbitrarily weak optical lattice commensurate with the atomic granularity, which leads to immediate pinning of the atoms. We map out the phase diagram and find that our measurements in the strongly interacting regime agree well with a quantum field description based on the exactly solvable sine-Gordon model. We trace the phase boundary all the way to the weakly interacting regime where we find good agreement with the predictions of the 1D Bose-Hubbard model. Our results open up the experimental study of quantum phase transitions, criticality, and transport phenomena beyond Hubbard-type models in the context of ultracold gases