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

The importance of forest structure for carbon fluxes of the Amazon rainforest

Precise descriptions of forest productivity, biomass, and structure are essential for understanding ecosystem responses to climatic and anthropogenic changes. However, relations between these components are complex, in particular for tropical forests. We developed an approach to simulate carbon dynamics in the Amazon rainforest including around 410 billion individual trees within 7.8 million km2. We integrated canopy height observations from space-borne LIDAR in order to quantify spatial variations in forest state and structure reflecting small-scale to large-scale natural and anthropogenic disturbances. Under current conditions, we identified the Amazon rainforest as a carbon sink, gaining 0.56 GtC per year. This carbon sink is driven by an estimated mean gross primary productivity (GPP) of 25.1 tC ha−1 a−1, and a mean woody aboveground net primary productivity (wANPP) of 4.2 tC ha−1 a−1. We found that successional states play an important role for the relations between productivity and biomass. Forests in early to intermediate successional states are the most productive, and woody above-ground carbon use efficiencies are non-linear. Simulated values can be compared to observed carbon fluxes at various spatial resolutions (>40 m). Notably, we found that our GPP corresponds to the values derived from MODIS. For NPP, spatial differences can be observed due to the consideration of forest successional states in our approach. We conclude that forest structure has a substantial impact on productivity and biomass. It is an essential factor that should be taken into account when estimating current carbon budgets or analyzing climate change scenarios for the Amazon rainforest

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

Climate and parameter sensitivity and induced uncertainties in carbon stock projections for European forests (using LPJ-GUESS 4.0)

Understanding uncertainties and sensitivities of projected ecosystem dynamics under environmental change is of immense value for research and climate change policy. Here, we analyze sensitivities (change in model outputs per unit change in inputs) and uncertainties (changes in model outputs scaled to uncertainty in inputs) of vegetation dynamics under climate change, projected by a state-of-the-art dynamic vegetation model (LPJ-GUESS v4.0) across European forests (the species Picea abies, Fagus sylvatica and Pinus sylvestris), considering uncertainties of both model parameters and environmental drivers. We find that projected forest carbon fluxes are most sensitive to photosynthesis-, water-, and mortality-related parameters, while predictive uncertainties are dominantly induced by environmental drivers and parameters related to water and mortality. The importance of environmental drivers for predictive uncertainty increases with increasing temperature. Moreover, most of the interactions of model inputs (environmental drivers and parameters) are between environmental drivers themselves or between parameters and environmental drivers. In conclusion, our study highlights the importance of environmental drivers not only as contributors to predictive uncertainty in their own right but also as modifiers of sensitivities and thus uncertainties in other ecosystem processes. Reducing uncertainty in mortality-related processes and accounting for environmental influence on processes should therefore be a focus in further model development

Trade-Offs for Climate-Smart Forestry in Europe Under Uncertain Future Climate

Forests mitigate climate change by storing carbon and reducing emissions via substitution effects of wood products. Additionally, they provide many other important ecosystem services (ESs), but are vulnerable to climate change; therefore, adaptation is necessary. Climate-smart forestry combines mitigation with adaptation, whilst facilitating the provision of many ESs. This is particularly challenging due to large uncertainties about future climate. Here, we combined ecosystem modeling with robust multi-criteria optimization to assess how the provision of various ESs (climate change mitigation, timber provision, local cooling, water availability, and biodiversity habitat) can be guaranteed under a broad range of climate futures across Europe. Our optimized portfolios contain 29% unmanaged forests, and implicate a successive conversion of 34% of coniferous to broad-leaved forests (11% vice versa). Coppices practically vanish from Southern Europe, mainly due to their high water requirement. We find the high shares of unmanaged forests necessary to keep European forests a carbon sink while broad-leaved and unmanaged forests contribute to local cooling through biogeophysical effects. Unmanaged forests also pose the largest benefit for biodiversity habitat. However, the increased shares of unmanaged and broad-leaved forests lead to reductions in harvests. This raises the question of how to meet increasing wood demands without transferring ecological impacts elsewhere or enhancing the dependence on more carbon-intensive industries. Furthermore, the mitigation potential of forests depends on assumptions about the decarbonization of other industries and is consequently crucially dependent on the emission scenario. Our findings highlight that trade-offs must be assessed when developing concrete strategies for climate-smart forestry

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

The role of ecosystem transpiration in creating alternate moisture regimes by influencing atmospheric moisture convergence

The terrestrial water cycle links the soil and atmosphere moisture reservoirs through four fluxes: precipitation, evaporation, runoff, and atmospheric moisture convergence (net import of water vapor to balance runoff). Each of these processes is essential for human and ecosystem well-being. Predicting how the water cycle responds to changes in vegetation cover remains a challenge. Recently, changes in plant transpiration across the Amazon basin were shown to be associated disproportionately with changes in rainfall, suggesting that even small declines in transpiration (e.g., from deforestation) would lead to much larger declines in rainfall. Here, constraining these results by the law of mass conservation, we show that in a sufficiently wet atmosphere, forest transpiration can control atmospheric moisture convergence such that increased transpiration enhances atmospheric moisture import and resulting water yield. Conversely, in a sufficiently dry atmosphere increased transpiration reduces atmospheric moisture convergence and water yield. This previously unrecognized dichotomy can explain the otherwise mixed observations of how water yield responds to re-greening, as we illustrate with examples from China's Loess Plateau. Our analysis indicates that any additional precipitation recycling by additional vegetation increases precipitation but decreases local water yield and steady-state runoff. Therefore, in the drier regions and early stages of ecological restoration, the role of vegetation can be confined to precipitation recycling, while once a wetter stage is achieved, additional vegetation enhances atmospheric moisture convergence and water yield. Evaluating the transition between regimes, and recognizing the potential of vegetation for enhancing moisture convergence, are crucial for characterizing the consequences of deforestation and for motivating and guiding ecological restoration.Comment: Revised version; response to the reviewers can be found in Appendix A, 39 pages, 11 figures, 2 table

Detecting impacts of extreme events with ecological in situ monitoring networks

Extreme hydrometeorological conditions typically impact ecophysiological processes on land. 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 whether the density of existing ecological in situ networks is sufficient for analysing the impact of extreme events, and 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 networks, 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 eight largest (typically very large) extreme events; but only a  ≥  50 % chance of capturing the 39 largest events. These findings are consistent with probability-theoretic considerations, but the slopes of the decay rates deviate due to temporal autocorrelation 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 theoretical considerations, we find that today's systematically designed networks (i.e. NEON) reliably detect the largest extremes, but that the extreme event detection rates are not higher than would be achieved by randomly designed networks. Spatio-temporal expansions of ecological in situ monitoring networks should carefully consider the size distribution characteristics of extreme events if the aim is also to monitor the impacts of such events in the terrestrial biosphere