Nonlinear dynamics of river runoff elucidated by horizontal visibility graphs

Horizontal Visibility Graphs (HVGs) are a recently developed method to construct networks from time series. The values of the time series are considered as the nodes of the network and are linked to each other if there is no larger value between them, such as they can “see” each other. The network properties reflect the nonlinear dynamics of the time series. For some classes of stochastic processes and for periodic time series, analytical results can be obtained for network-derived quantities such as the degree distribution, the local clustering coefficient distribution, the mean path length, and others. HVGs have the potential to discern between deterministic-chaotic and correlated-stochastic time series. Here, we investigate the sensitivity of the HVG methodology to properties and pre-processing of real-world data, i.e., time series length, the presence of ties, and deseasonalization, using a set of around 150 runoff time series from managed rivers at daily resolution from Brazil with an average length of 65 years. We show that an application of HVGs on real-world time series requires a careful consideration of data pre-processing steps and analysis methodology before robust results and interpretations can be obtained. For example, one recent analysis of the degree distribution of runoff records reported pronounced sub-exponential “long-tailed” behavior of North American rivers, whereas another study of South American rivers showed hyper-exponential “short-tailed” behavior resembling correlated noise. We demonstrate, using the dataset of Brazilian rivers, that these apparently contradictory results can be reconciled by minor differences in data-preprocessing (here: small differences in subtracting the seasonal cycle). Hence, data-preprocessing that is conventional in hydrology (“deseasonalization”) changes long-term correlations and the overall runoff dynamics substantially, and we present empirical consequences and extensive simulations to investigate these issues from a HVG methodological perspective. After carefully accounting for these methodological aspects, the HVG analysis reveals that the river runoff dataset shows indeed complex behavior that appears to stem from a superposition of short-term correlated noise and “long-tailed behaviour,” i.e., highly connected nodes. Moreover, the construction of a dam along a river tends to increase short-term correlations in runoff series. In summary, the present study illustrates the (often substantial) effects of methodological and data-preprocessing choices for the interpretation of river runoff dynamics in the HVG framework and its general applicability for real-world time series.Fil: Lange, Holger. Norwegian Institute of Bioeconomy Research; NoruegaFil: Sippel, Sebastian. Norwegian Institute of Bioeconomy Research; NoruegaFil: Rosso, Osvaldo Aníbal. Instituto Universidad Escuela de Medicina del Hospital Italiano; Argentina. Universidad de Los Andes; Chile. Universidade Federal de Alagoas; Brasil. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Robust detection and attribution of climate change under interventions

Fingerprints are key tools in climate change detection and attribution (D&A) that are used to determine whether changes in observations are different from internal climate variability (detection), and whether observed changes can be assigned to specific external drivers (attribution). We propose a direct D&A approach based on supervised learning to extract fingerprints that lead to robust predictions under relevant interventions on exogenous variables, i.e., climate drivers other than the target. We employ anchor regression, a distributionally-robust statistical learning method inspired by causal inference that extrapolates well to perturbed data under the interventions considered. The residuals from the prediction achieve either uncorrelatedness or mean independence with the exogenous variables, thus guaranteeing robustness. We define D&A as a unified hypothesis testing framework that relies on the same statistical model but uses different targets and test statistics. In the experiments, we first show that the CO2 forcing can be robustly predicted from temperature spatial patterns under strong interventions on the solar forcing. Second, we illustrate attribution to the greenhouse gases and aerosols while protecting against interventions on the aerosols and CO2 forcing, respectively. Our study shows that incorporating robustness constraints against relevant interventions may significantly benefit detection and attribution of climate change

Drought, Heat, and the Carbon Cycle: a Review

Purpose of the Review Weather and climate extremes substantially affect global- and regional-scale carbon (C) cycling, and thus spatially or temporally extended climatic extreme events jeopardize terrestrial ecosystem carbon sequestration. We illustrate the relevance of drought and/or heat events (“DHE”) for the carbon cycle and highlight underlying concepts and complex impact mechanisms. We review recent results, discuss current research needs and emerging research topics. Recent Findings Our review covers topics critical to understanding, attributing and predicting the effects of DHE on the terrestrial carbon cycle: (1) ecophysiological impact mechanisms and mediating factors, (2) the role of timing, duration and dynamical effects through which DHE impacts on regional-scale carbon cycling are either attenuated or enhanced, and (3) large-scale atmospheric conditions under which DHE are likely to unfold and to affect the terrestrial carbon cycle. Recent research thus shows the need to view these events in a broader spatial and temporal perspective that extends assessments beyond local and concurrent C cycle impacts of DHE. Summary Novel data streams, model (ensemble) simulations, and analyses allow to better understand carbon cycle impacts not only in response to their proximate drivers (drought, heat, etc.) but also attributing them to underlying changes in drivers and large-scale atmospheric conditions. These attribution-type analyses increasingly address and disentangle various sequences or dynamical interactions of events and their impacts, including compensating or amplifying effects on terrestrial carbon cycling.publishedVersio

Have precipitation extremes and annual totals been increasing in the world’s dry regions over the last 60 years?

Daily precipitation extremes and annual totals have increased in large parts of the global land area over the past decades. These observations are consistent with theoretical considerations of a warming climate. However, until recently these trends have not been shown to consistently affect dry regions over land. A recent study, published by Donat et al. (2016), now identified significant increases in annual-maximum daily extreme precipitation (Rx1d) and annual precipitation totals (PRCPTOT) in dry regions. Here, we revisit the applied methods and explore the sensitivity of changes in precipitation extremes and annual totals to alternative choices of defining a dry region (i.e. in terms of aridity as opposed to precipitation characteristics alone). We find that (a) statistical artifacts introduced by data pre-processing based on a time-invariant reference period lead to an overestimation of the reported trends by up to 40 %, and that (b) the reported trends of globally aggregated extremes and annual totals are highly sensitive to the definition of a "dry region of the globe". For example, using the same observational dataset, accounting for the statistical artifacts, and based on different aridity-based dryness definitions, we find a reduction in the positive trend of Rx1d from the originally reported +1.6 % decade−1 to +0.2 to +0.9 % decade−1 (period changes for 1981–2010 averages relative to 1951–1980 are reduced to −1.32 to +0.97 % as opposed to +4.85 % in the original study). If we include additional but less homogenized data to cover larger regions, the global trend increases slightly (Rx1d: +0.4 to +1.1 % decade−1), and in this case we can indeed confirm (partly) significant increases in Rx1d. However, these globally aggregated estimates remain uncertain as considerable gaps in long-term observations in the Earth's arid and semi-arid regions remain. In summary, adequate data pre-processing and accounting for uncertainties regarding the definition of dryness are crucial to the quantification of spatially aggregated trends in precipitation extremes in the world's dry regions. In view of the high relevance of the question to many potentially affected stakeholders, we call for a well-reflected choice of specific data processing methods and the inclusion of alternative dryness definitions to guarantee that communicated results related to climate change be robust.Have precipitation extremes and annual totals been increasing in the world’s dry regions over the last 60 years?publishedVersio

Reverse engineering model structures for soil and ecosystem respiration: the potential of gene expression programming

Accurate model representation of land-atmosphere carbon fluxes is essential for climate projections. However, the exact responses of carbon cycle processes to climatic drivers often remain uncertain. Presently, knowledge derived from experiments, complemented with a steadily evolving body of mechanistic theory provides the main basis for developing such models. The strongly increasing availability of measurements may facilitate new ways of identifying suitable model structures using machine learning. Here, we explore the potential of gene expression programming (GEP) to derive relevant model formulations based solely on the signals present in data by automatically applying various mathematical transformations to potential predictors and repeatedly evolving the resulting model structures. In contrast to most other machine learning regression techniques, the GEP approach generates "readable" models that allow for prediction and possibly for interpretation. Our study is based on two cases: artificially generated data and real observations. Simulations based on artificial data show that GEP is successful in identifying prescribed functions with the prediction capacity of the models comparable to four state-of-the-art machine learning methods (Random Forests, Support Vector Machines, Artificial Neural Networks, and Kernel Ridge Regressions). Based on real observations we explore the responses of the different components of terrestrial respiration at an oak forest in south-east England. We find that the GEP retrieved models are often better in prediction than some established respiration models. Based on their structures, we find previously unconsidered exponential dependencies of respiration on seasonal ecosystem carbon assimilation and water dynamics. We noticed that the GEP models are only partly portable across respiration components; the identification of a "general" terrestrial respiration model possibly prevented by equifinality issues. Overall, GEP is a promising tool for uncovering new model structures for terrestrial ecology in the data rich era, complementing more traditional modelling approaches

Multidisciplinary Design Analysis of Reusable European VTHL and VTVL Booster Stages

While initially met with skepticism, launch vehicles with reusable stages are now an established and successful part of the global launch market. Thus, there is a need to analyze and assess the possibility of such a system being designed and built in Europe. Accordingly, in 2016 the German Aerospace Center (DLR) initiated a study on reusable first stages named ENTRAIN (European Next Reusable Ariane). Within this study two return method categories, respectively vertical take-off, vertical landing (VTVL) and vertical take-off, horizontal landing (VTHL) with winged stages, were investigated. First, preliminary design tools were used to identify promising configurations and in the second phase more specialized and extensive analyses were conducted for subsystems of special interest. From this second phase, the results of the evaluation of two areas are presented: Structure as well as system dynamics, guidance and control. The results of these analyses together with previously published results from other subsystems increase the confidence in the designs proposed and evaluated within the ENTRAIN study as well as in the general understanding of the technical factors driving the design of reusable stages

Detecting impacts of extreme events with ecological in situ monitoring networks

Extreme hydrometeorological conditions typically impact ecophysiological processes of terrestrial vegetation. Satellite based observations of the terrestrial biosphere provide an important reference for detecting and describing the spatiotemporal development of such events. However, in-depth investigations of ecological processes during extreme events require additional in-situ observations. The question is if the density of existing ecological in-situ networks is sufficient for analyzing the impact of extreme events, or what are expected event detection rates of ecological in-situ networks of a given size. To assess these issues, we build a baseline of extreme reductions in the Fraction of Absorbed Photosynthetically Active Radiation (FAPAR), identified by a new event detection method tailored to identify extremes of regional relevance. We then investigate the event detection success rates of hypothetical networks of varying sizes. Our results show that large extremes can be reliably detected with relatively small network, but also reveal a linear decay of detection probabilities towards smaller extreme events in log-log space. For instance, networks with ≈ 100 randomly placed sites in Europe yield a ≥ 90 % chance of detecting the largest 8 (typically very large) extreme events; but only a ≥ 50 % chance of capturing the largest 39 events. These finding are consistent with probability-theoretic considerations, but the slopes of the decay rates deviate due to temporal autocorrelation issues and the exact implementation of the extreme event detection algorithm. Using the examples of AmeriFlux and NEON, we then investigate to what degree ecological in-situ networks can capture extreme events of a given size. Consistent with our theoretic considerations, we find that today's systematic network designs (i.e. NEON) reliably detects the largest extremes. But the extreme event detection rates are not higher than they would be achieved by randomly designed networks. Spatiotemporal expansions of ecological in-situ monitoring networks should carefully consider the size distribution characteristics of extreme events if the aim is also to monitor their impacts in the terrestrial biosphere

Climate Extremes and their Impact on Ecosystem-Atmosphere Interactions

Extreme weather and climate events (summarised as "climate extremes" from here onwards) are a crucial aspect of Earth's climatic variability. However, climate extremes are frequently associated with adverse impacts on socio-economic and ecological systems. For example, heat in combination with drought may severely affect the functioning of terrestrial ecosystems, and in some cases these events have the potential to undo several years of ecosystem carbon sequestration. Moreover, the intensity and frequency of several types of climate extremes, such as heat, cold, and heavy rainfall, have been changing in recent years. These changes are projected to continue in the 21st century, thus raising concerns about the capacity of ecological and socio-economic systems to cope with these events in the future. Nonetheless, our scientific understanding of climate extremes and the mechanistic pathways through which these events propagate into ecological or socio-economic systems, remains limited. The impact of climate extremes varies widely depending on their type and spatio-temporal structure, and these impacts are mediated by the vulnerability and exposure of the system under scrutiny. Therefore, the quantification of these phenomena, and the attribution to their respective drivers across space and time is often ambiguous. Accordingly, closing scientific knowledge gaps and improving methodologies to scrutinise climate extremes and their impacts constitutes a research priority of high societal relevance. The overarching objective of the present PhD thesis is to improve the quantification of, and contribute to the understanding of climate extremes and their impact on ecosystem-atmosphere interactions. To address these objectives, the thesis relies on joint analyses and integration of observation-based datasets and model ensemble simulations. Specifically, the thesis explores (1) a wide range of generic statistical-methodological considerations, (2) approaches to enable sound process-oriented model ensemble simulations using observation-based constraints, towards (3) a comprehensive attribution of ecosystem impacts arising from climate extremes. 1. Statistical quantification of extremes in observed or simulated spatio-temporal gridded datasets (Part I). An investigation and quantification of extremes in spatio-temporal datasets requires robust statistical methodologies and diagnostics. Therefore, the thesis scrutinises statistical methods, both empirically and analytically, to explore recent changes in temperature and precipitation extremes in gridded observations. These analyses reveal that conventional statistical methods that are based on a reference period standardisation might induce substantial biases in spatially aggregated estimates of extremes. For example, the occurrence of extremes that exceed two standard deviations in standardised data could be overestimated by 48.2% outside a given reference period of 30 years in independent and identically distributed Gaussian data. Analytical corrections for these kinds of statistical errors are derived in the thesis. Because climate extremes are inevitably rare in temporally and spatially limited observational records, ensemble simulations constitute an indispensable and complementary tool to scrutinise climate extremes from a statistical perspective, circumventing small sample issues in observations. Hence, the thesis also illustrates how model ensembles can be used as surrogate observations to benchmark statistical methods and metrics for an accurate assessment of climate extremes in observations. 2. Observation-based constraints improve model ensemble simulations of climate extremes and ecosystem impacts (Part II). Climate model ensemble simulations generated for the purpose of quantifying and attributing climate extremes typically exhibit biases in their output that hinder any straightforward simulation or assessment of impacts. Therefore, I develop, apply, and evaluate tools to constrain climate model ensembles based on observational diagnostics related to land-atmosphere interactions. The application of these constraints simultaneously reduces multivariate biases in model ensembles and thus might offer a novel route to bias correction for climate impact simulations and analyses of climate extremes. 3. Extremes events in the terrestrial biosphere: drivers and attribution (Part III). Linking or attributing extreme responses in the terrestrial biosphere to climatic drivers is not straightforward because respective analyses often rely on small sample sizes or even singular events in observations. Therefore, I construct an ensemble of climate-ecosystem impact simulations, constrained by observational diagnostics developed in Part II, that is designed (a) to systematically investigate and attribute changes in the intensity and frequency of simulated ecosystem productivity extremes ("EPEs") to the respective drivers, and (b) to assess the effect of timing and seasonal interaction of EPEs in the terrestrial biosphere. Thus, a perspective centred on ecosystem impacts is adopted. An analysis of these simulations reveals that (a) recent trends in the intensity of EPEs in Europe are contrasting seasonally, i.e. spring EPEs show consistent trends towards increased carbon uptake, while trends in summer EPEs are predominantly negative (higher net carbon release under drought and heat in summer) or close to neutral. Furthermore, the analyses reveal that (b) spring-summer interacting carbon cycle effects due to climate extremes and thus their timing plays an important role in shaping EPEs in Europe. These interacting effects include both partial compensation of drought or heat wave induced carbon losses in summer due to increased carbon uptake in the preceding spring (driven by higher temperatures), and conversely, spring "carry-over" effects into summer arising from depleted soil moisture that exacerbates summer carbon losses. In conclusion, the thesis lays out a comprehensive framework for systematically quantifying and attributing the impacts of climate extremes in the terrestrial biosphere using joint analyses of observations and model ensembles. The thesis shows that firstly, scrutinising statistical methods and diagnostics, and evaluating observation-based constraints on model ensembles, are key to an improved understanding as well as quantification of climate extremes and their impacts. Secondly, a consequent probabilistic interpretation of climate-ecosystem model ensemble simulations offers novel perspectives on the mechanistic pathways and interacting effects of terrestrial ecosystem responses to climate extremes