Early warning signs of critical transitions -- The α\alpha-stable case

Statistical early warning signs can be used to identify an approaching bifurcation in stochastic dynamical systems and are now regularly employed in applications concerned with the identification of potential rapid, non-linear change or tipping points. However, the reliability of these early warning signs relies on a number of key mathematical assumptions, most notably the presence of Gaussian noise. We here show that for systems driven by non-Gaussian, $\alpha$-stable noise, the classical early warning signs of rising variance and autocorrelation are not supported by mathematical theory and their use poses the danger of spurious, false-positive results. To address this, we provide a generalized approach by introduce the scaling factor $\gamma_X$ as an alternative early warning sign. We show that in the case of the Ornstein-Uhlenbeck process, there exists a direct inverse relationship between $\gamma_{X}$ and the bifurcation parameter, telling us that $\gamma_{X}$ will increase as we approach the bifurcation. Our numerical simulations confirm theoretical results and show that our findings generalize well to non-linear, non-equilibrium systems. We thus provide a generalized, robust and applicable statistical early warning sign for systems driven by Gaussian and non-Gaussian $\alpha$-stable noise

A novel probabilistic risk analysis to determine the vulnerability of ecosystems to extreme climatic events

We present a simple method of probabilistic risk analysis for ecosystems. The only requirements are time series—modelled or measured—of environment and ecosystem variables. Risk is defined as the product of hazard probability and ecosystem vulnerability. Vulnerability is the expected difference in ecosystem performance between years with and without hazardous conditions. We show an application to drought risk for net primary productivity of coniferous forests across Europe, for both recent and future climatic conditions

Quantifying the impact of key factors on the carbon mitigation potential of managed temperate forests

Background: Forests mitigate climate change by reducing atmospheric CO2-concentrations through the carbon sink in the forest and in wood products, and substitution effects when wood products replace carbon-intensive materials and fuels. Quantifying the carbon mitigation potential of forests is highly challenging due to the influence of multiple important factors such as forest age and type, climate change and associated natural disturbances, harvest intensities, wood usage patterns, salvage logging practices, and the carbon-intensity of substituted products. Here, we developed a framework to quantify the impact of these factors through factorial simulation experiments with an ecosystem model at the example of central European (Bavarian) forests. Results: Our simulations showed higher mitigation potentials of young forests compared to mature forests, and similar ones in broad-leaved and needle-leaved forests. Long-lived wood products significantly contributed to mitigation, particularly in needle-leaved forests due to their wood product portfolio, and increased material usage of wood showed considerable climate benefits. Consequently, the ongoing conversion of needle-leaved to more broad-leaved forests should be accompanied by the promotion of long-lived products from broad-leaved species to maintain the product sink. Climate change (especially increasing disturbances) and decarbonization were among the most critical factors influencing mitigation potentials and introduced substantial uncertainty. Nevertheless, until 2050 this uncertainty was narrow enough to derive robust findings. For instance, reducing harvest intensities enhanced the carbon sink in our simulations, but diminished substitution effects, leading to a decreased total mitigation potential until 2050. However, when considering longer time horizons (i.e. until 2100), substitution effects became low enough in our simulations due to expected decarbonization such that decreasing harvests often seemed the more favorable solution. Conclusion: Our results underscore the need to tailor mitigation strategies to the specific conditions of different forest sites. Furthermore, considering substitution effects, and thoroughly assessing the amount of avoided emissions by using wood products, is critical to determine mitigation potentials. While short-term recommendations are possible, we suggest risk diversification and methodologies like robust optimization to address increasing uncertainties from climate change and decarbonization paces past 2050. Finally, curbing emissions reduces the threat of climate change on forests, safeguarding their carbon sink and ecosystem services

A generic pixel-to-point comparison for simulated large-scale ecosystem properties and ground-based observations: an example from the Amazon region

Comparing model output and observed data is an important step for assessing model performance and quality of simulation results. However, such comparisons are often hampered by differences in spatial scales between local point observations and large-scale simulations of grid cells or pixels. In this study, we propose a generic approach for a pixel-to-point comparison and provide statistical measures accounting for the uncertainty resulting from landscape variability and measurement errors in ecosystem variables. The basic concept of our approach is to determine the statistical properties of small-scale (within-pixel) variability and observational errors, and to use this information to correct for their effect when large-scale area averages (pixel) are compared to small-scale point estimates. We demonstrate our approach by comparing simulated values of aboveground biomass, woody productivity (woody net primary productivity, NPP) and residence time of woody biomass from four dynamic global vegetation models (DGVMs) with measured inventory data from permanent plots in the Amazon rainforest, a region with the typical problem of low data availability, potential scale mismatch and thus high model uncertainty. We find that the DGVMs under- and overestimate aboveground biomass by 25 % and up to 60 %, respectively. Our comparison metrics provide a quantitative measure for model–data agreement and show moderate to good agreement with the region-wide spatial biomass pattern detected by plot observations. However, all four DGVMs overestimate woody productivity and underestimate residence time of woody biomass even when accounting for the large uncertainty range of the observational data. This is because DGVMs do not represent the relation between productivity and residence time of woody biomass correctly. Thus, the DGVMs may simulate the correct large-scale patterns of biomass but for the wrong reasons. We conclude that more information about the underlying processes driving biomass distribution are necessary to improve DGVMs. Our approach provides robust statistical measures for any pixel-to-point comparison, which is applicable for evaluation of models and remote-sensing products

Standardized drought indices in ecological research: why one size does not fit all

Defining and quantifying drought is essential when studying ecosystem responses to such events. Yet, many studies lack either a clear definition of drought, and/or erroneously assume drought under conditions within the range of “normal climatic variability” (c.f. Slette et al., 2019). To improve the general characterization of drought conditions in ecological studies, Slette et al. (2019) propose that drought studies should consistently relate to the local climatic context, assessing whether reported drought periods actually constitute extremes in water availability

Variation in stem mortality rates determines patterns of above-ground biomass in Amazonian forests: implications for dynamic global vegetation models

Understanding the processes that determine above-ground biomass (AGB) in Amazonian forests is important for predicting the sensitivity of these ecosystems to environmental change and for designing and evaluating dynamic global vegetation models (DGVMs). AGB is determined by inputs from woody productivity [woody net primary productivity (NPP)] and the rate at which carbon is lost through tree mortality. Here, we test whether two direct metrics of tree mortality (the absolute rate of woody biomass loss and the rate of stem mortality) and/or woody NPP, control variation in AGB among 167 plots in intact forest across Amazonia. We then compare these relationships and the observed variation in AGB and woody NPP with the predictions of four DGVMs. The observations show that stem mortality rates, rather than absolute rates of woody biomass loss, are the most important predictor of AGB, which is consistent with the importance of stand size structure for determining spatial variation in AGB. The relationship between stem mortality rates and AGB varies among different regions of Amazonia, indicating that variation in wood density and height/diameter relationships also influences AGB. In contrast to previous findings, we find that woody NPP is not correlated with stem mortality rates and is weakly positively correlated with AGB. Across the four models, basin-wide average AGB is similar to the mean of the observations. However, the models consistently overestimate woody NPP and poorly represent the spatial patterns of both AGB and woody NPP estimated using plot data. In marked contrast to the observations, DGVMs typically show strong positive relationships between woody NPP and AGB. Resolving these differences will require incorporating forest size structure, mechanistic models of stem mortality and variation in functional composition in DGVMs

Effects of climate extremes on the terrestrial carbon cycle : concepts, processes and potential future impacts

This article is protected by copyright. All rights reserved. Acknowledgements This work emerged from the CARBO-Extreme project, funded by the European Community’s 7th framework programme under grant agreement (FP7-ENV-2008-1-226701). We are grateful to the Reviewers and the Subject Editor for helpful guidance. We thank to Silvana Schott for graphic support. Mirco Miglivacca provided helpful comments on the manuscript. Michael Bahn acknowledges support from the Austrian Science Fund (FWF; P22214-B17). Sara Vicca is a postdoctoral research associate of the Fund for Scientific Research – Flanders. Wolfgang Cramer contributes to the Labex OT-Med (n° ANR-11- LABX-0061) funded by the French government through the A*MIDEX project (n° ANR-11-IDEX-0001-02). Flurin Babst acknowledges support from the Swiss National Science Foundation (P300P2_154543).Peer reviewedPublisher PD